tracing value-added and double counting in gross exportsfirst, we provide a unified and transparent...
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NBER WORKING PAPER SERIES
TRACING VALUE-ADDED AND DOUBLE COUNTING IN GROSS EXPORTS
Robert KoopmanZhi Wang
Shang-Jin Wei
Working Paper 18579http://www.nber.org/papers/w18579
NATIONAL BUREAU OF ECONOMIC RESEARCH1050 Massachusetts Avenue
Cambridge, MA 02138November 2012
The views in the paper are those of the authors and may not reflect the views of the USITC, its Commissioners,or any other organization that the authors are affiliated with. We thank William Powers for his contributionsin the early stage of this research, Peter Dixon, Kei-Mu Yi and Zhu Kunfu for constructive and generousdiscussions, the editor (Penny Goldberg) and five referees of this journal and numerous conferenceand seminar participants for valuable comments, Paul Bernhard and Ravinder Ubee for efficient researchassistance, and Nikhil Patel and Joy Glazener for editorial assistance. The authors declare that theyhave no relevant or material interests that relate to the research described in this paper. The viewsexpressed herein are those of the author and do not necessarily reflect the views of the National Bureauof Economic Research.
NBER working papers are circulated for discussion and comment purposes. They have not been peer-reviewed or been subject to the review by the NBER Board of Directors that accompanies officialNBER publications.
© 2012 by Robert Koopman, Zhi Wang, and Shang-Jin Wei. All rights reserved. Short sections oftext, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit,including © notice, is given to the source.
Tracing Value-added and Double Counting in Gross ExportsRobert Koopman, Zhi Wang, and Shang-Jin WeiNBER Working Paper No. 18579November 2012, Revised February 2013JEL No. F10
ABSTRACT
This paper proposes a framework for gross exports accounting that breaks up a country’s gross exportsinto various value-added components by source and additional double counted terms. By identifyingwhich parts of the official trade data are double counted and the sources of the double counting, itbridges official trade (in gross value terms) and national accounts statistics (in value added terms).Our parsimonious framework integrates all previous measures of vertical specialization and value-addedtrade in the literature into a unified framework. To illustrate the potential of such a method, we presenta number of applications including re-computing revealed comparative advantages and the magnifyingimpact of multi-stage production on trade costs.
Robert KoopmanResearch DivisionOffice of EconomicsUS International Trade Commission500 E Street SWWashington, DC [email protected]
Zhi WangResearch DivisionOffice of EconomicsUS International Trade Commission500 E Street SWWashington, DC [email protected]
Shang-Jin WeiGraduate School of BusinessColumbia UniversityUris Hall 6193022 BroadwayNew York, NY 10027-6902and [email protected]
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As different stages of production are now regularly performed in different countries,
intermediate inputs cross borders multiple times. As a result, traditional trade statistics become
increasingly less reliable as a gauge of the value contributed by any particular country. This
paper integrates and generalizes the many attempts in the literature at tracing value added by
country and measuring vertical specialization in international trade. We provide a unified
conceptual framework that is more comprehensive than the current literature. By design, this is
an accounting exercise, and does not directly examine the causes and the consequences of global
production chains. However, an accurate and well-defined conceptual framework to account for
value added by sources is a necessary step toward a better understanding of all these issues.
Supply chains can be described as a system of value-added sources and destinations.
Within a supply chain, each producer purchases inputs and then adds value, which is included in
the cost of the next stage of production. At each stage, the value-added equals the value paid to
the factors of production in the exporting country. However, as all official trade statistics are
measured in gross terms, which include both intermediate inputs and final products, they “double
count” the value of intermediate goods that cross international borders more than once. Such a
conceptual and empirical shortcoming of gross trade statistics, as well as their inconsistency with
the System of National Accounts (SNA) accounting standards, has long been recognized by both
the economics profession and policy makers. 1
Case studies on global value chains based on detailed micro data for a single product or a
single sector in industries such as electronics, apparel, and motor vehicles have provided detailed
examples of the discrepancy between gross and value-added trade. While enhancing our intuitive
understanding of global production chains in particular industries, they do not offer a
comprehensive picture of the gap between value-added and gross trade, and an economy’s
participation in cross-border production chains. Several researchers have examined the issue of
vertical specialization on a systematic basis, including the pioneering effort of Hummels, Ishii,
and Yi (2001) (HIY in subsequent discussion). They suggested that a country can participate in
vertical specialization in two ways: (a) uses imported intermediate inputs to produce exports; (b)
exports intermediate goods that are used as inputs by other countries to produce goods for export.
1 See, for example, Leamer et al. (2006), Grossman and Rossi-Hasberg(2008), and Lamy (October 2010).
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HIY proposed to measure the imported foreign content in a country’s exports based on a
country’s Input-Output (IO) table.
There are two key assumptions in HIY's foreign content (VS) estimation: the intensity in
the use of imported inputs is the same between production for exports and production for
domestic sales; and imports are 100% foreign sourced. The first assumption is violated in the
presence of processing exports, which is a significant portion of exports for a large number of
developing countries (Koopman, Wang and Wei, 2008 and 2012). The second assumption does
not hold when there is more than one country exporting intermediate goods.
A growing recent literature aims to estimate value-added trade using global Inter-Country
Input-Output (ICIO) tables based on the Global Trade Analysis Project (GTAP) and World
Input-Output database (WIOD), such as Daudin, Rifflart, and Schweisguth (2011), Johnson and
Noguera (2012) and Stehrer, Foster, and de Vries (2012). Most these papers discuss the
connections between their works with HIY, but are more closely related to the factor content
trade literature, except Koopman et al. (2010). By integrating the literature on vertical
specialization and the literature on trade in value added, this paper makes the following
contributions:
First, we provide a unified and transparent mathematical framework to completely
decompose gross exports into its various components, including exports of value added,
domestic value added that returns home, foreign value added, and other additional double
counted terms. Measures of vertical specialization and trade in value-added in the existing
literature can be derived from this framework and expressed as some linear combinations of
these components. We show why some existing measures are special cases of the generalized
measures in our framework and why some have to be modified from their original definitions in
a more general multi-country framework with unrestricted intermediate trade.
Second, rather than simply excluding double counted items from official trade statistics,
we provide an accounting formula that quantifies different types of double counted items for the
first time in the literature. Knowing the relative importance of different double counted items in a
country’s gross exports can help us to gauge the depth and pattern of that country’s participation
in global production chains. For example, in some sectors, China and the United States may have
a similar amount of value added exports. However, the composition of the double counted terms
can be very different. For China, the double counted terms may show up primarily in the form of
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the use of foreign components (e.g., foreign product designs or machinery) in the final goods that
China exports. For the United States, the double counted terms may show up primarily in the
form of domestic value added finally returned and consumed at home (e.g., product designs by
Apple that is used in the final Apple products produced abroad but sold in the U.S. market). The
structure of these double counted items in addition to their total sums offer additional
information about the U.S. and China’s respective positions in the global value chain.
Third, our accounting framework establishes a precise relationship between value-added
measures of trade and official trade statistics, thus providing an observable benchmark for value-
added trade estimates, as well as a workable way for national and international statistical
agencies to remedy the missing information in current official trade statistics without
dramatically changing the existing data collection practices of national customs authorities.
Fourth, our estimated global ICIO table may better capture the international source and
use of intermediate goods than in previous databases in two ways. In estimating intermediate
goods in bilateral trade, we use end-use classifications (intermediate or final) of detailed import
statistics rather than the conventional proportionality assumptions. In addition, we estimate
separate input-output coefficients for processing trade in China and Mexico, the two major users
of such regimes in the world.
Finally, we report a number of applications to illustrate the potential of our approach to
reshape our understanding of global trade. For example, with gross trade data, the business
services sector is a revealed comparative advantage sector for India. In contrast, if one uses our
estimated domestic value added in exports instead, the same sector becomes a revealed
comparative disadvantage sector for India in 2004. The principal reason for this is how the
indirect exports of business services are counted in high-income countries. Consider Germany.
Most of its manufacturing exports embed German domestic business services. In comparison,
most of Indian goods exports use comparatively little Indian business services. Once indirect
exports of domestic business services are taken into account, Indian’s business service exports
become much less impressive relative to Germany and many other developed countries. As
another example, the value added decomposition shows that a significant portion of China’s
trade surplus to the United States in gross trade terms reflects indirect value added exports that
China does on behalf of Japan, Korea and Taiwan. While such stories have been understood in
qualitative terms, our framework offers a way to quantify these effects.
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This paper is organized as follows. Section 2 presents the conceptual framework of gross
exports accounting. Section 3 discusses database construction methods, especially on how to
estimate the required inter-country IO model from currently available data sources. Section 4
presents a number of illustrative applications. Section 5 concludes.
2. Gross Exports Accounting: Concepts and Measurement
2.1 Concepts
Four measures have been proposed in the existing literature:
1. The first measure of vertical specialization, proposed by HIY (2001), refers to the
imported content in a country’s exports. This measure, labeled as VS, includes both the directly
and indirectly imported input content in exports. In mathematical terms, it can be expressed as:
EAIAVS DM 1)( 2. A second measure, also proposed by HIY (2001) and labeled as VS1, looks at vertical
specialization from the export side, and measures the value of intermediate exports sent
indirectly through third countries to final destinations. However, HIY did not provide a
mathematical definition for VS1.
3. A third measure is the value of a country’s exported goods that are used as imported
inputs by the rest of the world to produce final goods that are shipped back to home. This
measure was proposed by Daudin et al (2011). Because it is a subset of VS1, they call it VS1*.
4. A fourth measure is value-added exports, which is value-added produced in source
country s and absorbed in destination country r. Johnson and Noguera (2012) defined this
measure and proposed to use the ratio of value-added exports to gross exports, or the "VAX
ratio" as a summary measure of value-added content of trade.
By definition, as value-added is a "net" concept, double counting is not allowed. As the
first three measures of vertical specialization all involve values that show up in more than one
country’s gross exports, they, by necessity, have to include some double-counted portions of the
official trade statistics. This implies that these two types of measures are not equal to each other
in general because double counting is only allowed in one of them. They become equal only in
some special cases as we will show later both analytically and numerically. In addition, these
existing measures are all proposed as stand-alone indicators. No common mathematical
(1)
-5
framework proposed in the literature provides a unified accounting for them and spells out their
relationships explicitly.
We provide below a unified framework that breaks up a country’s gross exports into the
sum of various components. The value added exports, VS, VS1, and VS1* are linear
combinations of these components. In addition, we show how one may generalize the VS
measure without the restrictive assumption made by HIY (no two-way trade in intermediate
goods). By properly including various double counted terms, our accounting is complete in the
sense that the sum of these well-identified components yields 100% of the gross exports.
For ease of understanding, we start with a discussion of a two-country one sector case in
Section 2.2. We relate the components of our decomposition formula with the existing measures
in the literature in Section 2.3. We provide several numerical examples in Section 2.4 to show
intuitively how our gross exports accounting equation works. Finally, we present the most
general G-country N-sector case.
2.2 Two-country case
Assume a two-country (home and foreign) world, in which each country produces in a
single tradable sector. The good in that sector can be consumed directly or used as an
intermediate input, and each country exports both intermediate and final goods to the other.
All gross output produced by country s must be used as either an intermediate good or a
final good, either at home or abroad. So country s’ gross output, xs, has to satisfy the following
accounting relationship:
(2) srssrsrssss yyxaxax , r,s = 1,2
Where ysr is the final demand in country r for the final good produced in Country s, and asr is the
input-output (IO) coefficient, describing units of intermediate goods produced in s used in the
production of one unit gross output in Country r. The two-country production and trade system
can be written as an inter-country input-output (ICIO) model as follows
(3)
2221
1211
2
1
2221
1211
2
1
yyyy
xx
aaaa
xx
,
With rearranging, we have
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(4)
2
1
2221
1211
2221
12111
2221
1211
2
1
yy
bbbb
yyyy
aIaaaI
xx
.
Since equation (4) takes into account both the direct and indirect use of a country’s gross
output as intermediate goods in the production of its own and foreign final goods, the
coefficients in the B matrix (Leontief inverse) are referred to as “total requirement coefficients”
in the input-output literature. Specifically, b11 is the total amount of Country 1’s gross output
needed to produce an extra unit of the final good in Country 1 (which is for consumption in both
Countries 1 and 2); b12 is the total amount of Country 1’s gross output needed to produce an
extra unit of the final good in Country 2 (again for consumption both at home and abroad).
Similar interpretations can be assigned to the other two coefficients in the B matrix.
We can break up each country’s gross output according to where it is ultimately absorbed
by rearranging both countries' final demand into a matrix format by source and destination, and
rewrite equation (4) as follows:
(5)
2222122121221121
2212121121121111
2221
1211
2221
1211
2221
1211
ybybybybybybybyb
yyyy
bbbb
xxxx
where ysr is as defined in equation (2), giving the final goods produced in country s and
consumed in country r. This final demand matrix in the middle of equation (5) is a 2 by 2 matrix,
summing along each row of the matrix equals ys, which represents the global use of the final
goods produced in each country as specified in equation (4).
We label the 2 by 2 matrix on the left hand side of equation (5) the “gross output
decomposition matrix.” It fully decomposes each country’s gross outputs according to where it is
absorbed. Each element xsr is the gross output in source country s necessary to sustain final
demand in destination country r. Summing along its row equals total gross output in country s, xs
as specified in equation (2). For example, it breaks up country 1’s gross output x1 into two parts:
x1 = x11 + x12. While x11 is the part of Country 1’s gross output that is ultimately absorbed in
country 1, x12 is the part of Country 1’s gross output that is ultimately absorbed in Country 2.
The RHS of equation (5) further decomposes x11 itself into two parts: x11=b11y11 + b12y21.
The first part, b11y11 is the part of Country 1’s gross output required to produce Country 1’s final
good that is consumed in Country 1. The second part, b12y21, is the part of Country 1’s gross
output that is exported as an intermediate good, and eventually returns home as part of Country
1’s imports from abroad (embedded in foreign final goods).
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Similarly, x12 can also be decomposed into two parts: x12 = b11y12 + b12y22. The first part,
b11y12 is the part of Country 1’s gross output that is used to produce exported final good that is
consumed abroad. b12y22 is the part of Country 1’s gross output that is exported as an
intermediate good and used in country 2 to produce final good that is consumed there. Of course,
x1 = x11 + x12 is nothing but Country 1’s total output. By assumption, they are produced by the
same technology and therefore have the same share of domestic value added.
By the same interpretation, Country 2’s gross output also can be first broken up into two
parts: 22212 xxx . x21 is Country 2's gross output that is ultimately absorbed in Country 1,
which can be in turn broken up to 21221121 ybyb . x22 is Country 2’s domestic absorption of its
own gross output, and can be further broken up to 22221221 ybyb .
By definition, to produce 1 unit of Country 1’s good, a11 units of domestic intermediate
good is used, and a21 units of imported intermediate good is used. Therefore, the fraction of
domestic output that represents the domestic value added in Country 1 is 21111 1 aav .
Similarly, the share of domestic value added in Country 2’s gross output is: 22122 1 aav .
Therefore, we can define a 2×2 direct value-added coefficient matrix as:
(6)
2
1
00v
vV .
Multiplying V with the Leontief inverse B produces the 2×2 value-added share (VB)
matrix, our basic measure of value-added shares by source of production.
(7)
222212
121111
bvbvbvbv
VB .
Within VB, v1b11 and 222bv denote the domestic value-added share of domestically produced
products for country 1 and country 2 respectively; v2b21 and 121bv denote the share of foreign
country’s value-added in the same goods.2 Because all value added must be either domestic or
foreign, the sum along each column is unity:
(8) 1222121212111 bvbvbvbv .
2 Note that the VB matrix is not any arbitrary share matrix, but rather the one that reflects the underlying production structure embedded in the ICIO model specified in equations (3). It contains all the needed information on value-added production by source.
-8
Given the assumption on the input-output coefficients, there is no difference in the share
of domestic value added in Country 1’s production for goods absorbed at home versus its
production for exports.3 Therefore, the total domestic value added in Country 1’s gross output is
simply v1x1; it is country 1's GDP by definition.
The total value added in Country 1’s gross outputs can be easily broken up into two parts
based on where it is ultimately absorbed: 12111111 xvxvxv where v1x11 is the domestic value
added that is ultimately absorbed at home, and v1x12 is the domestic value added that is
ultimately absorbed abroad.
The last part, v1x12, is also Country 1’s exports of value added. It is instructive to
decompose the last item further. Since 2212112111121 ybvybvxv , Country 1’s exports of value
added has two components: Country1’s value added embedded in Country 1’s exports of final
good that is absorbed in Country 2 (v1b11y12); and Country 1’s value added in its exports of
intermediate good that is used by Country 2 to produce final good that is ultimately locally
consumed (v1b12y22).
Note that v1x12 is conceptually the same as Country 1’s value added exports as defined by
Johnson and Noguera (2012) except that we express it as the sum of two components related
only to the final demand in the two countries. To summarize, Country 1’s and 2's "value-added
exports" are, respectively:
(9)
Intuitively, there are at least two reasons for a country’s exports of value added to be
smaller than its gross exports to the rest of the world. First, the production for its exports may
contain foreign value added or imported intermediate goods (a). Second, part of the domestic
value added that is exported may return home after being embodied in the imported foreign
goods rather than being absorbed abroad (b). In other words, exports of value added are a net
concept; it has to exclude from the gross exports both foreign value added and the part of
domestic value added that is imported back to home.
3 Such an assumption is maintained by HIY (2001), Johnson and Noguera (2012), and Daudin et al (2011). One might allow part of the production for exports (processing exports) to take on different input-output coefficients. Such a generalization is pursued by Koopman, Wang, and Wei (2012), who have worked out a generalized formula for computing the share of domestic value added in a country’s gross exports when processing trade is prevalent.
212221121221221
221211211112112
ybvybvxvVTybvybvxvVT
-9
Identifying and estimating these double counted terms in gross exports have important
implications for measuring each country's position in global value-chains. For example, two
countries can have identical ratios of value added exports to gross exports but very different
ratios of (a) and (b). Those countries that are mainly upstream in global production chains, such
as product design, tend to have a large value of (b) but a small value of (a). In comparison, those
countries mainly specializing in assembling imported components to produce final products tend
to have a small value of (b) but a big value of (a). However, the existing literature lacks a
uniform and transparent framework to compute exports of value added, part (a) and part (b)
simultaneously. We venture to do this next. Without loss of generality, let us work with country
1's gross exports first:
(10) 2121212 xaye
It says that country 1’s exports consist of final goods and intermediate goods. Combining (10)
with equation (8), we have
(11) 21221212112121121221211221212111
21221221211112212121112121221211112 ))((xabvxabvybvybvybvybv
xabvxabvybvybvxaybvbve
A step by step proof of 1211212112122121212111 xabvybvybvxabv can be found in appendix A.
Here we give the economic intuition behind it. The total value of country 1's intermediate
exports must include two types of value. First, it must include all value added by Country 1 in
its imports from Country 2. To see this, we note that in order for exported value produced by
Country 1 to come back through its imports, it must have first been embodied in Country 1’s
intermediate exports, which is 12112121121 xabvybv . Second, it must include all value added
generated in Country 1 that is absorbed in Country 2 after being used as intermediate inputs by
Country 2, which is 22121 ybv .
Note that multiplying the Leontief inverse with intermediate goods exports leads to some
double counting of gross output and thus some value terms in exports. However, in order to
account for 100% of the value of country 1's intermediate goods exports and to identify what is
double counted, we have to include them into the accounting equation first. By decomposing the
last two terms further, we can see precisely what is double counted. Using the gross output
identity (equation (2)) 12111111 exayx and 21222222 exayx , it is easy to show that
121
11111
111 )1()1( eayax 211
22221
222 )1()1( eayax (12)
-10
111
11)( yaI is the gross output needed to sustain final goods that are both produced and
consumed in country 1, using domestically produced intermediate goods; deducting it from
country 1's total gross output, what is left is the gross output needed to sustain country 1's
production of its gross exports e12. Therefore the two terms in right hand side of equation (12)
both have straightforward economic meanings. We can further show that
111
111111111
112112 )1()1( yaybyaab (see proof, also in Appendix A), which is the total gross
output needed to sustain final goods both produced and consumed in country 1, but using
intermediate goods that originated in Country 1 and shipped to Country 2 for processing before
being re-imported by Country 1 (gross output sold indirectly in the domestic market). These two
parts plus 2112 yb sum to x11 in equation (5), which is the gross output of country 1 absorbed in
country 1 to sustain its domestic final demand both directly and indirectly. It indicates that
Country 1's domestic final demand is satisfied by three production channels: (1) 111
11)( yaI is
part of country 1's gross output sold directly in the domestic market that is consumed there; (2)
2112 yb is part of country 1's gross output used as intermediate goods by country 2 to produce final
goods that is consumed in country 1; (3) 111
112112 )1( yaab is part of country 1's gross output used
as intermediate goods by country 2 to produced intermediate goods that is exported to country 1
to produce final goods in country 1 that is consumed there. They are all needed to sustain the
domestic final demand in country 1, but they differ in terms of how they participate in
international trade.
Replacing x1 by 121
11111
11 )1()1( eaya and x2 by 211
22221
22 )1()1( eaya in
equation (11), and rearranging terms, we can fully decompose Country 1's gross exports into its
various value-added and double counted components as follows:
(13)
211
2212212221
221221212212
121
1121121111
112112121121
2212112111122121211112
)1(])1([)1(])1([
][
eaabvyaabvybveaabvyaabvybv
ybvybvebvebve
.
While the algebra to arrive at equation (13) may be a bit tedious, expressing a country’s
gross exports as the sum of these eight terms on the right hand side of equation (13) is very
useful. We go over their economic interpretations systematically.
The first two terms in equation (13) (or the two terms in the first square bracket) are
value-added exports, i.e. country 1's domestic value-added absorbed outside country 1.
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The third term, 21121 ybv is country 1's domestic value-added that is initially embodied in
its intermediate exports but is returned home as part of Country 1’s imports of the final good.
The fourth term, 111
1121121 )1( yaabv , is also Country 1’s domestic value added that is initially
exported by Country 1 as part of its intermediate goods to Country 2, but then is returned home
via its intermediate imports from country 2 to produce final goods that is absorbed at home. Both
the third and the fourth terms are domestic value added produced in Country 1, exported to
Country 2, but then return to and stay in Country 1. Both are counted at least twice in trade
statistics as they first leave Country 1 for Country 2, and then leave Country 2 for Country 1 (and
ultimately stay in Country 1). Note that the value represented by these two terms can be
embodied in trade transactions that cross borders back and forth more than twice as long as they
originate in Country 1and are ultimately consumed in Country 1.
The fifth term, 121
1121121 )1( eaabv , may be called a “pure double counted term.” The
reason for labeling it as such will become clear after we present a similar dissection of Country
2’s gross exports and a further decomposition of this term. This term only occurs when both
countries export intermediate goods. If at least one country does not export intermediate goods
(i.e., no two-way trade in intermediate goods), this terms disappears.
The sixth term, 12212 ybv , is the foreign value-added in country 1's gross exports of final
goods; and the seventh term, 221
2212212 )1( yaabv , is the foreign value-added in country 1's
gross exports of intermediate goods. They both ultimately go back to the foreign country and
consumed there.
The eighth (and the last) term is another pure double counted item in country 1's gross
exports. Similar to the 5th term, this term would disappear if at least one country does not export
intermediate goods.
In a similar way, we can express Country 2's gross exports as a sum of eight terms:
(14)
121
1121121111
112112121121
211
2212212221
221221212212
2122211212212222112121
)1(])1([)1(])1([
][
eaabvyaabvybveaabvyaabvybv
ybvybvebvebve
Comparing equations (13) and (14), there are a few noteworthy features. First, the 3rd, 4th
and 5th terms in Country 1’s gross exports (13) are identical to the 6th, 7th, and 8th terms in
Country 2’s exports (14), and vice versa. This means that, the value added that is initially
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111
111111
1121122112221212111
11112112221212111111
)1(]})1([{)(
yavyaabybybybvybybybybvxvGDP
produced and exported by Country 1 but then re-imported by Country 1, is exactly the same as
foreign value added in Country 2’s gross exports to Country 1. Symmetrically, the foreign value
added in Country 1’s gross exports to Country 2, is the same as Country 2’s value added, initially
produced and exported by Country 2, but re-appears as part of Country 1’s gross exports to
Country 2.
Second, while the 1st and 2nd terms in equations (13) and (14) constitute value-added
exports, all other terms are double counted components in a country's official exports statistics.
However, there are conceptually interesting differences among the 3rd and the 4th terms as the
first group, the 6th and the 7th terms as the second group, and the 5th and 8th terms as the third
group. The differences are revealed when comparing them to the two countries’ GDP. More
precisely, a country’s GDP is the sum of its value-added exports plus its domestic value-added
consumed at home:
The last term in each GDP equation is value-added produced and consumed at home that are not
related to international trade; while the first four terms in the bracket in each GDP equation are
exactly the same as the first four terms in equations (13) and (14). It is easy to show that the sum
of global GDP always equals global final demand:
Equations (15) and (16) show that the 3rd and 4th terms in equations (13) and (14) are
counted as part of the home country’s GDP (even though they are not part of the home country’s
exports of value added). Because they represent a country’s domestic value-added that is initially
exported but imported back and consumed in the initial producing country, they are part of the
value-added created by domestic production factors. The 6th and 7th terms represent the foreign
value added in a Country’s exports that are ultimately absorbed in the foreign country. They are
counted once as part of the foreign country's GDP in equations (15) and (16). In comparison,
because a combination of the part of GDP that is consumed at home and exports of value added
2122212122121111
2221212111221121 )1()1(yyxaxaxxaxax
xaaxaaxvxvGDPGDP
221
222221
2212211221212211212
22221221212211212222
)1(]})1([{)(
yavyaabybybybvybybybybvxvGDP
(15)
(16)
(17)
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yields 100% of a country’s GDP, the 5th and 8th terms are not part of either country’s GDP. In
this sense, they are “pure double counted terms.”
Subtracting global GDP from global gross exports using equations (13), (14), (15) and
(16) yields the following:
Equation (18) shows clearly that besides the value added produced and consumed at
home (in the last square bracket), which is not a part of either country's gross exports, the 6th and
7th terms in equations (13), ])1([ 221
22122112212 yaabybv , and the 6th and 7th terms in equation
(14) ])1([ 111
11211221121 yaabybv , are double counted only once as foreign value-added in the
other country's gross exports. Because the 3rd and 4th terms in (13) and (14) reflect part of the
countries’ GDP, they are not double counted from the global GDP point of view. In comparison,
both the 5th and 8th terms are counted twice relative to the global GDP since they are not a part of
either country’s GDP.
Third, the nature of the 5th and 8th terms can be better understood if we break them up
further. In particular, with a bit of algebra, they can be expressed as linear combinations of
components of the two countries’ final demand:
(19) ])1([)1( 111
11211212112122121121112112121
1121121 yaabvybvybvybvabeaabv
(20)4 ])1([)1( 221
22122121221221222112121221211
2212212 yaabvybvybvybvabeaabv
The four terms inside the square bracket on the RHS of equation (19) are exactly the
same as the first four terms in the gross exports accounting equation (13). A similar statement
can be made about the four terms inside the square bracket in equation (20) to gross export
accounting equation (14). This means that the 5th and the 8th terms double-count a fraction of
both a country's value added exports and its domestic value added that has been initially exported
but are eventually returned home. Just to belabor the point, unlike the other terms in Equation
(13) that are parts of some countries’ GDP, the 5th and the 8th terms over-count the values that are
already captured by other terms in gross exports. Again, this feature suggests that they are “pure
double counted terms.”
4 Proofs of equations (18), (19) and (20) are provided in Appendix A.
])1()1([)1(2)1(2])1([])1([
221
222111
111211
2212212121
1121121
221
22122112212111
11211221121212112
yavyaveaabveaabvyaabybvyaabybvGDPGDPee
(18)
-14
Note, if Country 2 does not export any intermediate goods, then 21a = 21b =0, and the
entire RHS of equations (20) and (19) would vanish. Alternatively, if Country 1 does not export
intermediate goods, then 12a = 12b = 0, the entire RHS of equations (19) and (20) would also
vanish. In other words, the 5th and 8th terms exist only when two-way trade in intermediate goods
exist so that some value added is shipped back and forth as a part of intermediate trade between
the two countries. Because the eight components of equations (13) and (14) collectively
constitute 100% of a country's gross exports, missing any part, including the two pure double
counted terms, would yield an incomplete accounting of the gross exports.
Finally, while the 5th and 8th terms in Equation (13) are (double counted) values in
intermediate goods trade that are originated in Countries 1 and 2, respectively, we cannot directly
see where they are absorbed. By further partitioning the 5th and 8th terms, we can show where
they are finally absorbed and interpret the absorption by input/output economics. With a bit of
algebra, we can show5:
(21) ])1([])1([
)1()1(
111
112112211221221
221221122112
211
2212212121
1121121
yaabybayaabybaeaabveaabv
Therefore, the sum of 5th and 8th terms in equation (13) is equivalent to the sum of the four terms
in the RHS of equation (21). From equation (5), it is easy to see that the terms in the square
bracket in equation (21) are parts of x22 and x11, which are trade-related portions of gross output
that are both originally produced and finally consumed in the source country; therefore they are
part of each country's gross intermediate exports (a12x2 and a21x1). Since the value added
embodied in those intermediate goods are already counted once in the production of each
country's GDP (the 3rd and 4th, terms in equations (13) and (14)), they are double counted in
value-added (GDP) terms. As we pointed earlier, the exact same terms will also appear in
Country 2's official exports statistics.
Due to the presence of these types of conceptually different double counting in a
country's gross exports, we may separately define “domestic value added in exports”(part of a
country’s GDP in its exports) and “domestic content in exports.” The former excludes the pure
double counted intermediate exports that return home; whereas the latter is the former plus the
pure double counted term.
5 A step by step proof is in Appendix A.
-15
2.3 Using the accounting equation to generate measures of vertical specialization
We can relate the definitions of the three concepts to components in Equation (13).
Country 1’s exports of value added are the sum of the 1st and the 2nd term. It takes into account
both where the value is created and where it is absorbed. Country 1’s value added in its exports
is the sum of its exports of value added and the 3rd and the 4th terms. This concept takes into
account where the value is created but not where it is absorbed. Obviously, Country 1’s “value
added in its exports” is generally greater than its “exports of value added.” Finally, the domestic
content in Country 1’s exports is Country 1’s value added in its exports plus the 5th term, the
double counted intermediate goods exports that are originated in Country 1. This last concept
also disregards where the value is ultimately absorbed. By assigning the 5th term to the domestic
content in Country 1’s exports, and the 8th term to the foreign content in Country 1’s exports, we
can achieve the property that the sum of the domestic content and the foreign content yields the
total gross exports. We will justify these definitions in what follows.
We already show that the first two terms in Equation (13) correspond to value added
exports as proposed in Johnson and Noguera (2012). We now link other measures in the
literature to linear combinations of the components in the same gross exports accounting
equation. Following HIY’s original ideas, Koopman, Wang and Wei (2008 and 2012) have
shown that gross exports can be decomposed into domestic content and foreign content/vertical
specialization (VS) in a single country IO model without two-way international trade in
intermediate goods. If we were to maintain HIY’s assumption that Country 1 does not export
intermediate good (i.e., 12a = 12b = 0), then the two pure double counted terms, or the 5th and the
8th terms in equation (13) are zero. In this case, we can easily verify that the sum of the last four
terms in equation (13) is identical to the VS measure in the HIY (2001) paper.
To remove the restriction that HIY imposed on intermediate trade, we have to determine
how to allocate the two pure double counted terms. We choose to allocate the double counted
intermediate exports according to where they are originally produced. That is, even though the
5th term in equation (13) reflects pure double counting, it nonetheless is originally produced in
Country 1 and therefore can be treated as part of Country 1’s domestic content. Similarly, we
allocate the 8th term to the foreign content in Country 1’s exports. Such a definition is consistent
with HIY’s original idea that a country’s gross exports consist of either domestic or foreign
content and the major role of their VS measure is to quantify the extent to which intermediate
-16
goods cross international boarder more than once. It is also computationally simple because the
share of domestic and foreign content can be obtained directly from the VB matrix.
However, since the 5th term reflects double counted intermediate goods in a country’s
gross exports, we may wish to exclude it if we are to consider which part of Country 1’s GDP is
exported. In particular, we define “domestic value added in Country 1’s gross exports”
(regardless of where the exports are ultimately absorbed) as the sum of the first four terms on the
RHS of equation (13). This variable can be shown to equal to 121
111 )1( eav , part of equation (12),
Country 1’s gross output identity.
(22)
])1([])1([
}]1)1[()()1()1{()1()]()1[()1(
)]([)1()()1()1(
111
112112211212212112111
111
11111211212212112111
111111222112111211111
111
222221221121121221121
111
222212212122112112121
111
212121
111121
1111
yaabybvybvybvyabvybvybvybv
ybayybaybaavybybybaybaav
ybybybybayavxayaveavDV
The derivation uses the property of inverse matrix 21121111 1)1( baba and 22121211)1( baba .
Following the same frame of thinking, we label only the sum of the 6th and 7th terms, a
subset of the foreign content, as the “foreign value added in Country 1’s exports,” and define
country 1’s VS as:
12111211
2212212221
22122112212122121 )1()1(])1([ ebveaabvyaabybvebvVS
The first two terms are foreign value-added or GDP in country 1's exports, and VS share of
country 1 equals 212bv . Therefore, such a measure of foreign content is a natural extension of
HIY's VS measure in a two-country world with unrestricted intermediate goods trade. Because
the VS share is defined this way, it is natural to define the domestic content share in country 1's
exports as 1- VS share or 111bv .
In a two-country world, Country 1’s VS1 is identical to its VS1* and Country 2’s VS:
121
1121121111
222112211212112111 )1(])1([*1VS1 eaabvyaabybvebvVS which is the sum of the 3rd, 4th, and 5th terms in equation (13). However, in a multi-country
setting to be discussed later, VS1* will only be a subset of VS1, and the latter will also include
some third country terms.
(23)
(24)
-17
2.4 Numerical examples
To enhance the intuition for our approach, we provide some numerical examples.
Example 1: Two countries, one sector, and only one country exports intermediate good
Consider a world consisting of two countries (USA and CHN) and a single sector of
electronics. The two countries have identical gross exports and identical value added exports
(and hence identical VAX ratios). The point of this example is to show that the structure of the
“double counted” values in gross exports contains useful information.
Both USA and CHN have a gross output of 200. USA’s total output consists of 150 units
of intermediate goods (of which, 100 units are used at home and 50 units are exported) and 50
units of final goods (of which 30 are consumed at home and 20 are exported).
CHN’s total output consists of 50 units of intermediate goods (all used at home) and 150
units of final goods (of which, 70 units are exported and 80 units are used at home). By
construction, both countries export 70 units of their output (50 units of intermediate goods + 20
units of final goods exported by USA, and 70 units of final goods exported by CHN).
The domestic value added in USA’s output is therefore 100 (=value of gross output 200 –
value of domestic intermediate good of 100). Note no foreign value is used in USA’s production.
The domestic value added in CHN’s output is also 100 (= value of gross output 200 -value of
domestic intermediate goods of 50 – value of imported intermediate goods of 50). The input-
output relationship can be summarized as follows:
200200
2
1
xx
,
25.0025.05.0
A,
5.005.0
V
The two-country production and trade system can be written as an inter-country input output
(ICIO) model as follows
80702030
200200
25.0025.05.0
2
1
xx
,
The Leontief inverse matrix and the VB matrix can be computed easily as
33.1067.02
2221
1211
bbbb
B ,
67.0033.01
VB
We can break up each country’s gross output according to where it is ultimately absorbed
by rearrange each country's final demand as follows:
-18
7.1063.933.937.106
67.106033.9303.534069.4660
80702030
33.1067.02
2221
1211
xxxx
It is easy to verify that 12111 xxx and 22212 xxx . USA’s value-added export is 46.7
(v1x12=0.5*93.33), where 20 (=v1b11y12=0.5*2*20, first term in equation (13)) is the amount of
USA’s value added in its export of final goods that is absorbed in CHN, and 26.7(=v1b12y22
=0.5*0.667*80, second term in (13)) is the amount of USA’s value added in its export of
intermediate goods that is also absorbed in CHN. The amount of USA’s value added that is
embedded in its export of intermediate goods but returns home as part of CHN's export of final
goods is 23.3 (=v1b12y21=0.5*0.667*70, the 3rd term in (13)). Using the terminology of Daudin et
al, USA's VS1*=23.3, the same as the estimates from our accounting equation (13).
By construction, foreign value added in USA’s exports equals zero (since CHN does not
export intermediate goods by assumption). It is easy to verify that the sum of USA’s exports of
value added (46.7) and the amount of returned value added (23.3) is 70, which is the value of its
gross exports.
For CHN, its value added exports (that are absorbed in USA) are also 46.7 (=v2b22y21
=0.5*1.333*70, first term in equation (14)). It is entirely embedded in CHN’s exports of final
good to. However, CHN does import intermediate goods from USA to produce both goods
consumed in CHN and goods exported to USA. The amount of USA’s value added used in the
production of CHN’s exports is 23.3(= 21121 ybv =0.5*0.667*70, the 6th term in equation (14)). The
sum of CHN’s exports of value added (46.7) and the foreign value added in its exports (23.3) is
70, which is the same as CHN’s gross exports.
In this example, both countries have identical gross exports and exports of value added,
and therefore identical VAX ratios. However, the reasons underlying why value added exports
deviate from the gross exports are different. For USA, the VAX ratio is less than one because
some of the value added that is initially exported returns home after being used as an
intermediate good by CHN in the latter’s production for exports. For CHN, the VAX ratio is less
than one because its production for exports uses intermediate goods from USA which embeds
USA’s value added.
In addition, the double counted items are also value added at some stage of production.
More precisely, the VS in CHN’s exports (23.3) is simultaneously a true value added from
-19
USA’s viewpoint as it is value added by USA in its exports to CHN (that returned home), but a
“double counted item” from CHN’s viewpoint as it is not part of CHN’s value added.
Since we assume that CHN does not export intermediate goods (or a21=0 and b21 = 0),
there is no channel for CHN’s gross output to be used by USA in its production and for CHNs
gross output to be first exported and then returned home. Therefore, our gross exports accounting
equation produces the same estimate for VS as the HIY’s formula, i.e:
3.2370)25.01(25.0)1(3.2370667.05.0)1( 112
1112112212112 eaaebvbv
Domestic value-added share for CHN's exports equals (70-23.3)/70 = 0.667 = v2b22=0.667. There
is no difference between HIY's measure and our method in such a case since there are no pure
double counting terms due to two way trade in intermediate goods. Both VS in USA and VS1* in
CHN are zero. But this equality will not hold when we remove the assumption of a21=0.
However, because there is domestic value-added embodied in USA's intermediate goods
exports that is eventually returned home, the domestic value-added share in USA's exports
equals to 1. As a result, using the VAX ratio (0.667) as a metric of the share of home country's
domestic value-added in its gross exports would produce an underestimate. The corresponding
ICIO table and more computation details can be found in online appendix C.
Example 2: Different Sequences of Trade for same final goods consumption and same value-
added contribution from each source country
Imagine the US trades in a good that has $1 million of US value added plus $100,000 of
value added from each of other 5 countries before the final good, priced at $1.5 million, is
consumed in the US. Let us consider two different production sequences of the supply chains.
Case 1: If each of the five countries sends the parts sequentially between them for
assembly before they enter the US, then total trade will be $100K + $200K + $300K + $400K +
$500K = $1.5 million.
Case 2: If the US exports it's part first, then the production proceed sequentially and the
final goods produced by the production chain shipped back to the US, the total trade will be $1m
+ $1.1m + $1.2m + $1.3m + $1.4m + $1.5m = $7.5 million.
Both cases yield the same value added but different amounts of gross trade. However, the
two sequences of trade will correspond to two different inter-country input-output (ICIO) tables.
We can attach concrete labels to the final product and the inputs to get more economic intuition.
-20
Let us think of the final product as a Barbie doll, and the inputs as hair (made by the United
States), head, body, hat, clothes, and shoes, respectively. The information about the sequence of
the production is embedded in the direct input-output matrix A. In the first case, if the hair is
attached by the U.S. at the last stage of production, it is an input to the “doll” industry. While in
the second case, if the hair is first exported to the country producing “head,” attached to the
“head” there, and re-exported to the next stage of production, it becomes an input to the “head”
industry. The two different organizations of the spatial and temporal connections of hair to head
show up in changed entries to the ICIO matrix, with inputs of hair to the "doll" industry falling in
the former recipient country ICIO coefficient in the first case, but inputs of hair rising in the
second country’s "head" industry and measured inputs of heads (now bulked up with the hair
value) rising in all head-using industries in all countries downstream from the initial head-
producing country to the final "doll" industry that uses heads. While a change in the first
country’s hair inputs from the final country’s doll industry to the second country’s head industry
in the direct I-O matrix A, the inverse (direct plus indirect request) matrix B will still capture that
the hair arrived via the heads. Due to the less direct route of hair to dolls is raising measured
inputs in all subsequent stages, as well as in the trade statistics, this case clearly show a rise in
gross imports and exports for those downstream of the head industry with only a redirection (not
an increase) in exports of hair even though value added is constant by assumption.
In Appendix C, we show how ICIO tables can be constructed for each of the two cases.
In each case, our decomposition formula decomposes the gross exports into value added by each
source country plus additional double counted terms. The results are reported in Table 1.
Because these are very simple examples, we can also decompose the gross exports in each case
by economic intuition (see Table 2). The results are identical to what our decomposition formula
generates. However, our analytical formula not only clearly shows the structure of a country's
value-added exports (exports in final goods (v1), in intermediate goods (v2) and indirect exports
via third countries (v3)), but also further splits the overall double counted amount to what is
domestic value-added initially exported and eventually returning home (v4), what is foreign
value-added (v7), and what is double counted due to intermediate goods imported from foreign
countries (v9). The additional detail provides more information about the structure of both the
value-added and the double counted trade. A more detailed two country supply chain example is
provided in online appendix D with additional economic intuition.
-21
2.5 The General Case of G Countries and N Sectors We now discuss the general case with any arbitrary number of countries and sectors. The
ICIO model, gross output decomposition matrix, value-added by source shares matrix, are given
succinctly by block matrix notations:
(25)
(26)
(27)
GGGGGGG
G
G
BVBVBV
BVBVBVBVBVBV
VB
21
22222212
11121111
With G countries and N sectors, A, and B are GN×GN matrices; V and VB are G×GN matrices.
Vs denotes a 1 by N row vector of direct value-added coefficient, Asr is a N×N block input-output
coefficient matrix, Bsr denotes the N×N block Leontief inverse matrix, which is the total
requirement matrix that gives the amount of gross output in producing country s required for a
one-unit increase in final demand in destination country r. Xsr is a N×1 gross output vector that
gives gross output produced in s and absorbed in r. Xs = G
rsrX is also a N×1 vector that gives
country s' total gross output. Ysr is a N×1 vector give final goods produced in s and consumed in r.
Ys = G
rsrY is also a N×1 vector that gives the global use of s’ final goods. Both the gross output
decomposition and final demand matrix in equation (26) are GN×G matrices.
GGGGG
G
G
G
rGr
G
rr
G
rr
GGGG
G
G
G Y
YY
BBB
BBBBBB
Y
Y
Y
AIAA
AAIAAAAI
X
XX
2
1
21
22221
11211
2
11
21
22221
11211
2
1
GGGG
G
G
GGGG
G
G
GGGG
G
G
YYY
YYYYYY
BBB
BBBBBB
XXX
XXXXXX
21
22221
11211
21
22221
11211
21
22221
11211
-22
Let sV̂ be a N by N diagonal matrix with direct value-added coefficients along the
diagonal. (Note sV̂ has a dimension that is different from Vs). We can define a GN by GN
diagonal value-added coefficient matrix as
(28)
GV
V
V
V
00
00
00
2
1
Using the similar intuition as we used to derive equation (9) in the two country one sector
case, we can obtain domestic value-added in a country's gross output by multiplying this value-
added coefficient matrix with the right hand side of equation (26), the gross output
decomposition matrix. This will result in a GN by G value-added production matrix
VBY as
G
rrGGrG
G
rrGrG
G
rrGrG
G
rrGr
G
rrr
G
rrr
G
rrGr
G
rrr
G
rrr
GGGG
G
G
G YBVYBVYBV
YBVYBVYBV
YBVYBVYBV
XXX
XXXXXX
V
V
V
BYV
21
22222122
11211111
21
22221
11211
2
1
00
00
00
ˆ
Elements in the diagonal columns give each country's production of value-added absorbed at
home. As in the two country case, exports of value-added can be defined as the elements in the
off-diagonal columns of this GN by G matrix as
Obviously, it excludes value-added produced by the home country that returns home after
being processed abroad. A country's total value-added exports to the world equal:
(31)
By rewriting equation (31) into three groups according to where and how the value-added
exports are absorbed, we obtain decomposition as follows:
G
ggrsgssrssr YBVXVVT
G
sr
G
ggrsgs
G
srsrs YBVVXVT
1*
(29)
(30)
(31)
-23
(32)6
G
srrt
G
rstsrsrr
G
srsrssr
G
srssss YBVYBVYBVVT
,*
This is the value-added export decomposition equation in terms of all countries’ final demands.
The first term is value-added in the country's final goods exports; the second term is value-added
in the country's intermediate exports used by the direct importer to produce final goods
consumed by the direct importer; and the third term is value-added in the country's intermediate
exports used by the direct importing country to produce final goods for third countries.
Comparing with equation (9), we can see clearly what is missing in our two country case: it is
the re-export of value-added via third countries, the last term of the RHS of equation (32),
because the distinction between value-added exports from direct and indirect sources only can be
made in a setting with three or more countries.
Define a country’s gross exports to the world as:
(33)
G
srsrrsr
G
srsrs YXAEE )(*
Using the logic similar to the derivation of equations (11), we can first decompose a country's
gross exports to its various components as follows:
(34)7
G
st
G
srrsrtst
G
st
G
srsrtst
G
sr
G
srsrssrsrssrss
s
G
srrsrsssss
XABVYBVXABVYBVVT
EBVEBVuE
}{}{*
***
Based on the gross output identity for each country *sssssss EXAYX , we have,
(35) *11 )()( ssssssss EAIYAIX *
11 )()( rrrrrrrr EAIYAIX
Replace Xs and Xr in equation (34), insert equation (32), we obtain the G country, N sector
generalized version of gross exports accounting equation as follows:
(36)
6 This value-added exports decomposition could also be done at the bilateral level; however, it is different from equation (15) in Johnson and Noguera (2012), who split bilateral gross exports to three groups. 7 The step by step proof is provided in online Appendix B.
G
srrrr
G
stsrtst
G
strrrr
G
srsrtst
G
st
G
srsrtst
G
srsss
G
srrssrsssss
G
srrssrsrssrs
G
srrt
G
rstsrsrr
G
srsrssr
G
srssss
EAIABVYAIABVYBV
EAIABVYAIABVYBV
YBVYBVYBVuE
*11
*11
,*
)(})({
)(})({
}{
-24
Equation (36) has nine terms. It is very similar to equations (13) and (14) in the two country case
with only one main difference. It has an additional term, representing indirect value-added
exports via third countries, in its value-added exports besides the two value-added terms that
directly absorbed by the direct importer. Therefore, the first three terms are value-added exports
(only two terms in the two country case). The 4th and 5th term in the second bracketed expression,
includes the source country's value-added in both its final and intermediate goods imports, which
are first exported but eventually returned and consumed at home, both of which are parts of the
source country's GDP but represent a double counted portion in official gross export statistics,
and have a similar economic interpretation as the 3rd and 4th terms in equations (13) and (14).
They differ from the two country case in that we have to account for the domestic value-added
returning home from each of the G-1 countries here, not just from Country 2. The 7th and 8th
terms in the third bracketed expression represent foreign value-added (GDP) in the source
country's gross exports, including foreign GDP embodied in both final and intermediate goods.
They differ from the 6th and 7th terms in equation (13) in the two country case in that equation
(36) further partitions each of the foreign value added (GDP) by individual country sources.
There are also two pure double counted terms, the 6th and the 9th terms in equation (36) as
equations (13) and (14), but they sum up the double counted portions of two way intermediate
trade from all bilateral routes, not just between Country 1 and 2. The complete gross exports
accounting made by equations (36) is also diagrammed in Figure 1.
Similar to the two country case, measures of vertical specialization can be expressed as
linear combination of the various components identified by equations (36) as follows:
(37)
This is the first five terms in equation (36) and clearly shows that a country's domestic value-
added in its exports is generally greater than its value-added exports in aggregate. The two
measures equal each other only in the case where there is no returned domestic value-added in
imports, i.e. when both
G
srrssrs YBV and ssss
G
srrssr YAIAB 1)(
are zero.
G
rs
G
srssss
G
srrssrsrssrsssssss VTYAIABVYBVVTEAIVDV *
1**
1 )()(
-25
(38)
G
st
G
srrsrtst
G
st
G
srsrtsts
G
srrsr
G
srrrr
G
stsrtst
G
strrrr
G
srsrtst
G
st
G
srsrtsts
XABVYBVEBV
EAIABVYAIABVYBVVS
*
*11 )()(
which is composed of the last three terms in equation (36).
We can verify that equation (38) is reduced to more familiar expressions in some special
cases. Using a single country IO model, Koopman, Wang and Wei (2008, 2012) have shown
(39) VS share = 1)( Dv AIAu 1)( DM AIuA
In the G-country world,
(40)8 VS share =
G
srssrssrsssssss
G
srrsr AIABVAIVuBVuBV 11 )()(
The last term in the last step can be interpreted as the adjustment made for domestic content
returned to the source country. Therefore, our foreign content measure of gross exports is a
natural generalization of HIY's VS measure in a multi-country setting with unrestricted
intermediate goods trade. Because uBVBV sss
G
srrsr
, it is natural to define a country's
domestic content in its exports as:
(41)
G
rsr
G
srs
G
srsrssrsrssrsssssss VTDVXABVYBVVTEBVDC **
This is the sum of the first 6 terms in equation (36).9 It shows that a country's domestic content
in its exports is generally greater than the part of its GDP in exports therefore is also greater than
its value-added exports in the aggregate. The three measures equal each other only in the case
where there is no returned domestic value in imports, i.e. when both
G
srrssrs YBV and
G
srsrssrs XABV are zero.
The second HIY measure of vertical specialization (VS1) measures the value of the
exported goods that are used as imported inputs by other countries to produce their exports.
Although an expression for such indirectly exported products has not been previously defined 8 See online appendix B for the step by step proof. 9 Note that the third term can be further decomposed into two terms (the 5th and 6th terms) in equation (36).
-26
mathematically in the literature, it can be specified based on some of the terms in our gross
exports accounting equations.
(42)
G
sr
G
srsrssrsrssrs
G
srtrt
G
rstsrs
G
srrt
G
rstsrs
G
srrsrss XABVYBVXABVYBVEBV
,,*VS1
This means HIY’s VS1 can be expressed as the third term in (36) plus the third and fifth terms in
equation (34). The second term in equation (42) measures how much domestic content in
exported goods from the source country is used as imported inputs to produce other countries’
intermediate goods exports. It also shows clearly that HIY's VS1 measure is generally greater
than indirect value-added exports because the latter only includes the first term of (42), but
excludes domestic content that is returned home and the value embodied in intermediate goods
exports via third countries (they are already counted as other countries' foreign content in these
third countries' exports), i.e.
(43) s
G
srrt
G
rstsrs VSYBV 1IV
,s
Compared with equation (24) of the definition of VS1 in the two-country case, two additional
terms (the first two terms) appear on the RHS of (42) because of the third country effect.
(44)
G
sr
G
srsrssrsrssrs
tsrssrss XABVYBVEBV*VS1
As equation (44) shows, we define VS1* as a subset of VS1 similar to Daudin et al. (2011), but
our definition differs from theirs as they include only domestic value-added returned home in
final goods imports (the first term in equation (44)) but exclude domestic content returned home
by being embodied in the imports of intermediate goods, the second term in equation (44).10 If
one omits the second term, then VS1* would be inconsistent with the core idea of measuring
vertical specialization from the export side, as it would fail to account for the source country’s
exports used by third countries to produce their export of intermediate goods. It would therefore
consistently under-estimate actual vertical specialization. To put it differently, the same
domestic content embodied in a country's intermediate goods exports manifests itself in
international trade flows in two ways: (a) as foreign content in other countries exports, and (b) as
the source country’s indirect exports of domestic content via a third country. In other words, the
foreign content in one country’s exports is the domestic content of another country embodied in
10 Note that the second term can be further decomposed into two terms (the 5th and 6th terms) in equation (36).
-27
its indirect exports. As an example, the Japanese content in the form of Japanese-made computer
chips used in China’s exports of electronic toys to the United States represents foreign content in
China’s exports, and it is also simultaneously Japan’s indirect exports of its domestic content to
the United States. While these two perspectives produce the identical numbers when aggregating
across all countries at the global level, their values for a given country can be very different.
Therefore, when measuring a country’s participation in vertical specialization it is useful to be
able trace the two perspectives separately. This is also why HIY proposed two measures of
vertical specialization, because a complete picture of vertical specialization and a county’s
position in a vertical integrated production network has to involve both measures. Indeed, for a
given country, the ratio of the two measures provides insight for the country's position in global
value chains. Downstream countries tend to have a higher share of vertical specialization from
the import side, i.e higher foreign content (VS) in their exports, while upstream countries tend to
have a higher share of vertical specialization from export side (VS1), higher share of exports via
third countries. In addition, as we show in both equations (13) and (36), ignoring domestic
content returning home via intermediate goods imports would leave the gross export accounting
incomplete.
Therefore, equation (36) provides a new way of thinking about the gross exports statistics.
It demonstrates that various double counted items in gross exports can be used to gauge the depth
of a country’s participation in global production chains. Simply stripping away double counted
items and focusing just on value added trade would miss such useful information. We have
already provided numerical examples earlier to illustrate the intuition of this point; now we have
laid out the accounting equation in a more general multi-country setting. It provides a transparent
framework that allows various value-added and double counted components in a country's
official gross exports statistics to be correctly identified and estimated.
Equation (36) (or Figure 1) also integrates the older literature on vertical specialization
with the newer literature on trade in value added, while ensuring that the sum of value-added
components from all sources and the additional double counted intermediate goods exports (due
to back-and-forth trade in intermediate goods) yields total gross exports. The previous vertical
specialization literature only decomposes gross exports into two components: domestic and
foreign content. In comparison, Equation (36) shows that a country’s domestic content can be
further broken up into sub-components that reveal the destinations for a country’s exported value
-28
added, including its own value-added that returns home in its imports and what is double counted
due to cross border intermediate goods trade. Similarly, equation (36) also traces out the foreign
content in a country’s exports to its sources.
Finally, note that we use a single subscript for the domestic content measure and two
subscripts for the trade in value-added measure. This is to suggest that the trade in value-added
measure holds for both aggregate and bilateral trade, while the gross export accounting equation
we propose only holds for a country's total exports to the world.
3. Data and results
3.1 The construction of an Inter-Country Input-output (ICIO) table and its data sources
To implement the above accounting method, we need an inter-country input output (ICIO)
table, that is, a database detailing international production and use for all flows of value added.
The database should specify (a) transactions of intermediate products and final goods within and
between each country at the industry level, (b) the direct value-added in production of each
industry in all countries, and (c) the gross output of each industry in all countries. Such an ICIO
table goes beyond a collection of single-country IO tables. It specifies the origin and destination
of all transaction flows by industry as well as every intermediate and/or final use for all such
flows. However, these tables are not available on a global basis, and in fact are rarely available at
the regional level. The available global databases, such as the GTAP Multi-Country Input-Output
(MCIO) tables, do not have enough detail on the cross-border supply and the use of goods to be
directly used to implement our methodological framework.
To provide a workable dataset and empirically conduct gross export decomposition, we
construct a global ICIO table for 2004 by integrating the GTAP database (version 7) and the
additional information from UN COMTRADE using a quadratic mathematical programming
model. The model (a) minimizes the deviation of the resulting new data set from the original
GTAP data, (b) ensures that supply and use balance for each sector and every country, and (c)
keeps all sectoral bilateral trade flows in the GTAP database constant. The new database covers
26 countries and 41 sectors11.
11 Tsigas, Wang and Gehlhar (2012) provides details on the construction of the database. The longer working paper lists the countries/regions and sectors in our sample and their concordance to the GTAP database.
-29
To estimate these detailed inter-industry and inter-country intermediate flows, we need to
(i) separate gross bilateral trade flows at the sector level in the GTAP database into intermediate,
consumption and investment goods trade flows, and (ii) allocate intermediate goods from a
particular country source to each sector it is used within all destination countries. We address the
first task by concording the three end-use categories defined by UN Broad Economic Categories
(BEC) to the 6-digit HS level bilateral trade data in COMTRADE. This differs from Johnson and
Noguera (2012) and Daudin, Rifflart, and Schweisguth (2011), who also transform the MCIO
table in the GTAP database into an ICIO table. However, they do not use detailed trade data to
identify intermediate goods in each bilateral trade flow, but apply a proportionality method
directly to the GTAP trade data; i.e., they assume that the proportion of intermediate to final
goods is the same for domestic supply and imported products.
The use of end-use categories to distinguish imports by use is becoming more widespread in
the literature and potentially avoids some noted deficiencies in the proportionality method.
Feenstra and Jensen (2009) use a similar approach to separate final goods from intermediates in
U.S. imports in their recent re-estimation of the Feenstra-Hanson measure of material off-
shoring. Dean, Fung, and Wang (2011) show that the proportionality assumption underestimates
the share of imported goods used as intermediate inputs in China’s processing trade. Nordas
(2005) stated that the large industrial countries have a higher share of intermediates in their
exports than in their imports, while the opposite is true for large developing countries. These
results imply that the intermediate content of imports differs systematically from the intermediate
content in domestic supply.
In theory, less distorted intermediate share estimates will provide a better row total control
for each block matrix of srA in the ICIO coefficient matrix A, thus improving the accuracy of the
most important parameters (the inter country IO coefficients) in an ICIO model. This is why
distinguishing imports by BEC may improve ICIO database quality over the proportionality
assumption. To precisely assess whether and how much the BEC method improves over the
proportionality approach, one would need the true inter-country IO coefficients as a “reference
point”, which unfortunately do not exist on a global scale. We will provide some evidence that
the two alternative ways to identify intermediate goods from bilateral trade flows in the literature
have a significant impact on trade cost when the magnification effects of multi-stage production
are taken into account in one of our application examples.
-30
3.2 Complete accounting of gross exports
Table 3 presents a complete accounting of each country’s gross exports in 2004 using
equation (36). The column numbers correspond to the order of each item in the equations and
also the box numbers in Figure 1. The first three columns also correspond to the three terms in
the RHS of equation (32).
We compute all these nine terms independently and verify that they sum to exactly 100
percent of gross exports. The resulting estimates constitute the first such decomposition in a
global setting and clearly highlight what is double counted in the official trade statistics. Column
(15) reports the percentage of double counting by adding columns (4) to (9). At the global level,
only domestic value added in exports absorbed abroad are value-added exports. In addition to
foreign content in exports, domestic content that returns home from abroad is also a part of
double counting in official trade statistics, since it crosses borders at least twice. Such returned
value added has to be separated from domestic value-added absorbed abroad in order to fully
capture multiple counting in official trade statistics. Therefore, for any country’s gross exports,
the double counting portion equals the share of gross exports in excess of the value-added
exports. We estimate this share to be about 25.6% of total world exports in 2004.
The accounting results reported in table 3 also provide a more detailed breakdown of
domestic content in exports than has been previously available in the literature. The variations in
the relative size of different components across countries provide a way to gauge the differences
in the role that countries play in global production networks. For example, for the United States,
the share of foreign value-added in its exports was only 9% (columns 7+8), while its own GDP
first exported then finally return home is large at 11.3% (columns 4+5), indicating that most of
its exports reflect its own domestic value added. In comparison, for China’s and Mexico's
processing exports, the share of foreign GDP in their gross exports is 46.5% and 55.8%
respectively, with an additional 10.1% and 7.6% of their gross exports coming from intermediate
goods produced in foreign countries (column 9), indicating domestic value added accounts for
less than half the value of both countries’ processing exports. More importantly, about half of the
double counting in U.S. exports – reflected as 1-VAX ratio (column 11) in column 15 - comes
primarily from its own domestic content returning home via imports (12.4% over 25.4%). In
contrast, almost all of the double counting in China's and Mexico's processing exports comes
from imported foreign content (56.6% over 56.9% and 63.4 over 63.7 respectively). These
-31
calculations highlight U.S. exporters and Chinese and Mexican processing exporters' respective
positions at the head and tail of global production chains.
The structure of double counted terms in each country's gross exports listed in columns (4)
through (9) offers additional information on how each country participates in vertical
specialization and its relative position in global production chains. For example, for Western EU
countries, about 40% of its double counted gross exports come from domestic content returned
home (7.4/18.9). In comparison, for most developing countries, the foreign content tends to
dominate, with only a very tiny portion of their domestic content returning home. Within foreign
content, Maquiladora producers in Mexico, export processing zones in China and Vietnam, tend
to have a large portion embodied in their final goods exports (37.6%, 34.1% and 24.4%,
respectively), reflecting their position as the assemblers of final goods in global production
chains. For developed and newly industrialized economies, the shares in intermediate goods
exports and the pure double counted portion due to multiple border crossing intermediate goods
trade are much higher. Similarly, upstream natural resource producers such as Australia & New
Zealand, Russia, Indonesia and Philippines, have a significant portion of their intermediate
exports used by other countries to produce their intermediate goods exports. This is also true for
upstream producers of manufacturing intermediates such as Japan.
To reiterate the connection of the nine basic components reported in the Table 3 to
measures in the existing literature by numerical estimates, column (11) reports the value-added
to gross exports (VAX) ratio proposed by Johnson and Noguera (2012) by adding up columns
(1), (2), and (3); column (12) list HIY's VS share by summing column (7) , (8) and (9). Column
(14) lists the share of domestic content extensively discussed in the vertical specialization
literature by summing columns (1) through (6); Finally, column (16) gives the share of vertical
trade by adding columns (12) and (13), which is an indicator of how intensively a country is
participating in the global production chain.
Comparing domestic content share estimates (Column 14) and Johnson & Noguera's
VAX ratio (Column 11) reported in table 3, we see interesting differences between high-income
countries and emerging market economies. For most emerging market economies, the numerical
difference of these two measures is quite small. This means that only a tiny part of domestic
content returns home for most countries. In comparison, for the United States, Western Europe
and Japan, the difference between domestic content share and the value added export share is
-32
more significant. This reflects the fact that advanced economies export relatively more upstream
components, and some of the value added embedded in these intermediate goods returns home as
part of other countries’ exports to the advanced economies. Such differences between high-
income countries and emerging market economies would not be apparent if one does not
compute the domestic content share and the VAX ratio separately.
4. Broad implications for a better understanding of global trade
The decomposition results have implications for a variety of research and policy
questions. In this section, to illustrate the potential importance of the decomposition, we briefly
discuss a few applications.
4.1 Revealed Comparative Advantage index based on gross and value-added trade
The concept of revealed comparative advantage (RCA for short), proposed by Balassa
(1965), has proven useful in many research and policy applications. In standard applications, it is
defined as the share of a sector in a country’s total gross exports relative to the world average of
the same sector in world exports. When the RCA exceeds one, the country is said to have a
revealed comparative advantage in that sector; when the RCA is below one, the country is said to
have a revealed comparative disadvantage in that sector. The problem of double counting of
certain value added components in the official trade statistics suggests that the traditional
computation of RCA could be noisy and misleading. The gross exports accounting exercise we
proposed in this paper provides a way to remove the distortion of double counting by focusing on
domestic value-added in exports. Because domestic value-added or GDP in a country’s exports
describes the characteristics of a country’s production (total domestic factor content in exports),
it does not depend on where the exports is absorbed. For those applications in which a
production-based RCA is the right measure, we can use GDP in exports to compute RCA.
We re-compute the RCA index at the country-sector level for all the countries and sectors
in our database. Due to space constraints, we select two sectors and compare the country
rankings of RCAs using both gross exports and domestic value-added in gross exports. In left
panel of Figure 2, we report the two sets of RCA indices for the finished metal products sector in
2004. Using gross exports data, both China and India show a strong revealed comparative
advantage (ranked the first and fourth, respectively, among the set of countries in our database,
-33
and with the absolute values of RCA at 1.94 and 1.29, respectively). However, when looking at
domestic value added in that sector’s exports, both countries ranking in RCA drop precipitously
to 7th and 15th place, respectively.12 In fact, for India, the sector has switched from being labeled
as a comparative advantage sector to a comparative disadvantage sector. Unsurprisingly, the
ranking for some other countries move up. For example, for the United States, not only does its
RCA ranking move up from 10th place under the conventional calculation to the 3rd place under
the new calculation, but its finished metal products industry also switches from being labeled as
a comparative disadvantage sector to a comparative advantage sector.
Another example is the “real estate and business services” sector (right panel of Figure
2). Using data on gross exports, India exhibits a strong revealed comparative advantage in that
sector on the strength of its unusually high share of business services exports in its overall
exports. However, once we compute RCA using domestic value-added in exports, the same
sector becomes a comparative disadvantage sector for India! One key reason for the change is
that business services in advanced countries are often exported indirectly by being embedded in
these countries manufacturing exports. Indeed, the RCA rankings for the United States, the
European Union and Japan all move up using data on the domestic value-added in exports.
Therefore, after taking into account indirect value added exports, the Indian share of the sector in
its exports becomes much less impressive (relative to other countries).
These examples illustrate the possibility that our understanding of trade patterns and
revealed comparative advantage could be modified substantially once we have the right statistics.
4.2 Magnification of trade costs from multi-stage production
As noted by Yi (2003, 2010), multi-stage production magnifies the effects of trade costs
on world trade. There are two separate magnification forces. The first exists because goods that
cross national borders multiple times incur tariffs and transportation costs multiple times. The
second exists because tariffs are applied to gross imports, even though value added by the direct
exporter may be only a fraction of this amount. Different ways of participating in global
production chain affects the extent to which different countries are affected by such cost
12 Sectoral value added here includes value produced by the factors of production employed in the finished metal products sector and then embodied in gross exports of all downstream sectors, rather than the value added employed in upstream sectors that are used to produce finished metal products in the exporting country. This distinction is particularly important in the business services sector, discussed next.
-34
magnification. However, Yi (2003) does not actually measure the magnification of tariffs,
though it is important to his simulation exercise.
Our gross export accounting method provides an ideal way to re-examine the
magnification issue. In Appendix E, we provide an illustrative calculation of the first order
magnification effect of using imported intermediate inputs to produce exports. It represents the
magnification effect if tariffs were the only factor that augments the trading costs. For instance,
we find that one additional stage of production increases trade costs of Vietnam’s merchandise
production by 80% of its standard tariff. Generally speaking, the magnification effect is stronger
for emerging market economies than for developed economies due to the lower domestic value-
added share in most developing countries’ manufacturing exports. In the same appendix, we also
show that global ICIO databases constructed by the BEC end-use classification versus the
proportionality assumption produce different trade cost magnification effects for a number of
countries.
4.3 Other applications
The set of examples discussed so far certainly does not exhaust the possible applications.
For example, the Federal Reserve Board and the IMF routinely compute effective exchange rates
using trade weights that are based on gross exports and imports. A conceptually better measure
should weight trading partners based on the relative importance in value added trade rather than
in gross trade terms. Our decomposition results make it feasible to do such computations.
As another example, for some research or policy questions, one might need to look at the
response of a country’s bilateral or multilateral trade to exchange rate changes. Once one
recognizes that there is a potential mismatch between trade in value added and trade in gross
terms, one would want to take this into account. Our decomposition allows for a correction.
As a further example, because a country’s gross exports embed value added from other
countries, its bilateral trade balance in value added terms can be very different from that in gross
trade terms. By our estimation, because China is the final assembler in a large number of global
supply chains, and it uses components from many other countries, especially East Asian
countries, its trade surplus with US and Western EU countries measured in value-added term is
41% and 49% less than that measured in gross terms in 2004. In contrast, Japan's trade surplus
with the U.S. and Western EU countries are 40% and 31% larger measured in value-added terms,
-35
because Japan exports parts and components to countries throughout Asia that are eventually
assembled into final products there and exported to the United States and Western EU countries.
5. Conclusions
We have developed a unified conceptual framework that can fully account for a country’s
gross exports by its various value-added and double counted components. This new framework
incorporates all previous measures of vertical specialization and value-added trade in the
literature while adjusting for the back-and-forth trade of intermediates across multiple borders.
With a full concordance between value-added and double counted components and official gross
trade statistics, it opens the possibility for the System of National Accounts (SNA) to accept the
concept of value-added trade without dramatically changing current practice of customs trade
data collection. This may in turn provide a feasible way for international statistical agencies to
report value-added trade statistics regularly in a relatively low cost fashion.
The creation of a database that encompasses detailed global trade in both gross and value-
added terms will allow us to move from a largely descriptive empirical exercise to analysis of the
causes and consequences of differences in supply chain participation. We show that conventional
analyses involving revealed comparative advantage, bilateral trade balance, trade cost or
effective real exchange rates can all benefit from our gross exports accounting results.
Better information at the sector level can improve our estimation. For instance, current
end use classifications, such as the UN BEC, need to be extended to dual used products and
services trade. In addition, methods also need to be developed to properly distribute imports to
domestic users either based on cross country statistical surveys or based on firm level and
Customs transaction-level trade data. We leave such sector level applications to future research.
References
Balassa, Bela. 1965. “Trade Liberalization and ‘Revealed’ Comparative Advantage.” Manchester School of Economic and Social Studies, 33, 99–123. Daudin, Guillaume, Christine Rifflart, and Danielle Schweisguth. 2011. “Who Produces for Whom in the World Economy?” Canadian Journal of Economics 44(4):1409-1538, November. Dean, Judy, K.C. Fang and Zhi Wang. 2011. “How Vertically Specialized is Chinese Trade.” Review of International Economics, 19(4):609-625.
-36
Feenstra, Robert and J. Bradford Jensen. 2009. “Evaluating Estimates of Materials Offshoring from U.S. Manufacturing.” NBER Working Paper 17916. Grossman, G. and E. Rossi-Hansberg. 2008. “Trading Tasks: A Simple Theory of Offshoring.” American Economic Review, 98:5, 1978-1997. Hummels, D., J. Ishii, and K. Yi. 2001. “The Nature and Growth of Vertical Specialization in World Trade.” Journal of International Economics 54:75–96.
Johnson, Robert, and Guillermo Noguera. 2012. “Accounting for Intermediates: Production Sharing and Trade in Value-added.” 86(2012):224-236, Journal of International Economics. Johnson, Robert, Rudolfs Bems, and Kei-Mu Yi. 2011. “"Vertical Linkages and the Collapse of Global Trade."American Economic Review, Papers and Proceedings,101:2, May. Koopman, Robert, Zhi Wang, and Shang-Jin Wei. 2008. “How Much Chinese Exports Is Really Made in China—Assessing Foreign and Domestic Value-added in Gross Exports.” NBER Working Paper 14109. Koopman, Robert, William Powers, Zhi Wang, Shang-Jin Wei. 2010. "Give Credit Where Credit Is Due: Tracing Value Added in Global Production Chains." NBER Working Paper No. 16426. Koopman, Robert, Zhi Wang and Shang-Jin Wei. 2012. “Estimating domestic content in exports when processing trade is pervasive." 99(2012):178-189, Journal of Development Economics. Nordas, Hildegunn. 2005. “International Production Sharing: A Case for a Coherent Policy Framework.” Discussion Paper No. 11, World Trade Organization. Stehrer, Robert, Neil Foster and Gaaitzen de Vries. 2012. “Value Added and Factors in Trade: A Comprehensive Approach.” Working Paper No. 7, World Input-output database. Tsigas, Marinos, Zhi Wang and Mark Gehlhar. 2012. "How a Global Inter-Country Input-Output Table with Processing Trade Account Can be constructed from GTAP Database." Unpublished. Wang, Zhi, William Powers, and Shang-Jin Wei. 2009. “Value Chains in East Asian Production Networks.” USITC Working Paper No. 2009-10-C, October. Yi, Kei-Mu. 2010. "Can Multistage Production Explain the Home Bias in Trade?" American Economic Review, 100(1):364-393. Yi, Kei-Mu. 2003. “Can Vertical Specialization Explain the Growth of World Trade?” Journal of Political Economy, 111(1): 52–102.
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Table 1. Decomposition of gross exports in different organization of global production
chain for same final goods delivery and value-added by source countries
Terms in
accounting
equation
Term 1
(v1)
Term 2
(v2)
Term 3
(v3)
Term 4
(v4)
Term 5
(v5)
Term 6
(v6)
Term
7 (v7)
Term
8 (v8)
Term
9 (v9)
Total
gross
exports
Case 1
C1 0 0 1 0 0 0 0 0 0 1
C2 0 0 1 0 0 0 0 0 1 2
C3 0 0 1 0 0 0 0 0 2 3
C4 0 0 1 0 0 0 0 0 3 4
C5 0 1 0 0 0 0 0 0 4 5
USA 0 0 0 0 0 0 0 0 0 0 Case 2
USA 0 0 0 10 0 0 0 0 0 10
C1 0 0 1 0 0 0 0 0 10 11
C2 0 0 1 0 0 0 0 0 11 12
C3 0 0 1 0 0 0 0 0 12 13
C4 0 0 1 0 0 0 0 0 13 14
C5 1 0 0 0 0 0 14 0 0 15
Note: The unit is $100K. Table 2 Intuitive accounting for the gross exports flows in numerical example 2
Value-
added input
intermediate input
gross output
value-added exports
gross exports
double counting
stage 1 country 1 100,000 0 100,000 100,000 100,000 0
stage 2 country 2 100,000 100,000 200,000 100,000 200,000 100,000
stage 3 country 3 100,000 200,000 300,000 100,000 300,000 200,000
stage 4 country 4 100,000 300,000 400,000 100,000 400,000 300,000
stage 5 country 5 100,000 400,000 500,000 100,000 500,000 400,000
stage 6 USA 1,000,000 500,000 1,500,000 0 0 0
stage 7 USA consumes all the final goods from stage 6, its own production
Total 1,500,000 1,500,000 3,000,000 500,000 1,500,000 1,000,000
Case 2
stage 1 USA 1,000,000 0 1,000,000 0 1,000,000 1,000,000
stage 2 country 1 100,000 1,000,000 1,100,000 100,000 1,100,000 1,000,000
stage 3 country 2 100,000 1,100,000 1,200,000 100,000 1,200,000 1,100,000
stage 4 country 3 100,000 1,200,000 1,300,000 100,000 1,300,000 1,200,000
stage 5 country 4 100,000 1,300,000 1,400,000 100,000 1,400,000 1,300,000
stage 6 country 5 100,000 1,400,000 1,500,000 100,000 1,500,000 1,400,000
stage 7 USA consumes all the final goods from stage 6- country 5's exports
total 1,500,000 6,000,000 7,500,000 500,000 7,500,000 7,000,000
-38
Figure 1 Accounting of gross exports: concepts
Note:
a. value-added exports by a country equals (1) + (2) +(3) .
b. GDP in exports (1) + (2) + (3) + (4) +(5).
c. domestic content in a country's exports equals (1) + (2) + (3) + (4) +(5)+(6).
d. (7)+(8)+(9) is labeled as VS, and (3) + (4)+(5)+(6) is part of VS1 labeled by HIY (2001).
e. (4) are also labeled as VS1* by Daudin et al (2011).
f. (4) through (9) involve value added that crosses national borders at least twice, and are the
sources of multiple counting in official trade statistics.13
13 (3) should not be included in double counting, because when this value crosses a border for the second time, it becomes foreign value in the direct importer’s exports. For this reason, it is not included as double counting to avoid an over-correction.
(6) double counted interme-
diate exports
produced at home
Gross exports (E)
Value-added exports (VT)
Foreign Content (VS)
(1) DV in direct final
goods exports
(3) DV in
intermediates re-exported to third
countries IV
(4) DV in
intermediates that returns
via final imports
(2) DV in
interme-diates
exports absorbed by direct importers
(5) DV in
interme-diates that returns via Interme-
diate imports
Domestic Content in intermediate exports that finally return home
(VS1*)
(7) FV in final
goods exports
(8) FV in
interme-diate goods
exports
(9) double counted interme-
diate exports
produced abroad
Domestic content (DC)
-39
Table 3 Accounting of gross exports, 2004
Country/region Value-added exports Domestic VA
return home
Pure
double
counting
Foreign VA
return foreign
countries
Pure
double
counting
Connection with existing measures
in Billions of US dollars
in direct final exports
in int. absorb by direct importers
in int. re-exports to third countries
in final exports
in int. exports
in int. exports produced in home
in final exports
in int. exports
in int. exports produced abroad
Total VAX ratio
VS share
VS1 share
DC share
Double count share
Share of Vertical trade
(0) (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16)
Advanced economies Aus-New Zealand 122.5 27 50.5 10.5 0.2 0.2 0.1 3.7 5.1 2.8 100 88 11.5 27.9 88.5 12 39.4 Canada 323 23.5 43 4 0.5 0.4 0.5 12.8 12 3.3 100 70.5 28.1 12.2 71.9 29.5 40.4 Western EU 1,575.50 38.1 38.1 5 3.1 3.4 0.9 4.8 4.3 2.4 100 81.1 11.4 20.9 88.6 18.9 32.3 Japan 618.9 38.4 34.2 12.2 1.4 1 0.5 4.8 3.7 3.7 100 84.9 12.2 30.8 87.8 15.1 43.1 United States 1,062.30 32.5 36.6 5.5 6.8 4.5 1.2 4.3 4.7 4 100 74.6 12.9 27 87.1 25.4 39.9 Asian NICs Hong Kong 121.7 27.2 35.7 9.1 0.4 0.1 0.1 10.2 9.9 7.4 100 71.9 27.5 19.5 72.5 28.1 47 Korea 283.1 29.5 25.3 10.4 0.3 0.2 0.4 13.1 9.9 10.8 100 65.2 33.9 23.2 66.1 34.8 57 Taiwan 219.8 19.2 25.9 13.1 0.2 0.1 0.5 12.4 12.5 16.1 100 58.2 41.1 27.1 58.9 41.8 68.2 Singapore 150.6 11 20.1 5.2 0.1 0.1 0.4 17 24.2 22.1 100 36.3 63.2 12.8 36.8 63.7 76 Emerging Asia China Normal 334.6 44.2 31.8 8.1 0.4 0.7 0.1 6.8 5.2 2.7 100 84.2 14.6 20.7 85.4 15.8 35.3 China Processing 336 28.8 12.6 1.7 0 0 0.3 34.1 12.4 10.1 100 43.1 56.6 4.3 43.4 56.9 60.9 China total 670.6 36.5 22.2 4.9 0.2 0.3 0.2 20.5 8.8 6.4 100 63.6 35.7 12.5 64.3 36.4 48.1 Indonesia 86.7 20 45.6 10.9 0.2 0.3 0.2 9.2 7.2 6.5 100 76.5 22.9 29 77.1 23.5 51.9 Malaysia 152 16.7 31.5 10.4 0.3 0.1 0.6 12.9 13.6 14 100 58.6 40.5 25 59.5 41.4 65.5 Philippines 50.1 17.6 27.8 12.4 0.1 0 0.2 10.8 14 17.1 100 57.8 41.9 29.4 58.1 42.2 71.2 Thailand 119.4 27.9 24.2 7.9 0.1 0.1 0.2 17.2 11.3 11.2 100 60 39.7 18.5 60.3 40 58.1 Vietnam 32.3 32.9 24.9 4.8 0 0.2 0.2 24.4 7.7 4.9 100 62.6 37.0 14.8 63.0 37.4 51.8 India 99.9 30.2 41.7 7.7 0.1 0.2 0.1 6.4 9.5 4.2 100 79.6 20.1 18.9 79.9 20.4 39 Other emerging Brazil 113 27.4 52.1 7.5 0.1 0.1 0.1 3.9 6.4 2.4 100 87 12.7 19.2 87.3 13 31.9 New EU countries 273.7 28.7 35.2 4.3 0.4 0.3 0.3 13.4 13.2 4.2 100 68.3 30.8 11.4 69.2 31.7 42.1 Mexico Normal 63.6 23.5 52.7 5.9 0.1 0.5 0.1 2.9 11.5 2.8 100 82.1 17.3 18 82.7 17.9 35.3 Mexico Processing 126.9 20.6 13.3 2.4 0 0 0.3 37.6 18.2 7.6 100 36.3 63.4 5.9 36.7 63.7 69.2 Mexico total 190.5 21.6 26.5 3.6 0.1 0.2 0.2 26 16 6 100 51.6 48.0 9.9 52.0 48.4 57.9 Russian 160.2 9.5 70.2 9.4 0.3 0.2 0.1 1.6 5.9 2.7 100 89.1 10.2 31.2 89.8 10.9 41.4 South Africa 61.4 23.1 50 8.5 0.1 0.1 0.1 5.3 8.9 4 100 81.6 18.2 24.2 81.8 18.4 42.4 World average 7,733.40 29.2 38.4 6.8 1.9 1.5 0.6 8.7 7.7 5.1 100 74.4 21.5 21.5 78.5 25.6 43
Source: Authors’ estimates Notes: All columns are expressed as a share of total gross exports. Column (11) = (1)+(2)+(3); column (12) =(7)+(8)+(9);Column (14)= (1)+(2)+(3) +(4)+(5)+(6);Column (15) equal sum from (4) to (9).
-40
Figure 2 Value-added-adjusted Revealed Comparative Advantage Indicators
A1
Online Appendices
Appendix A: Derivation details for major equations in the two country, one sector model
Based on the property of inverse matrix, we have:
2221
1211
2221
1211
2221
1211
2221
1211
11
1001
11
aaaa
bbbb
bbbb
aaaa
(A1)
Therefore, the following identities hold:
21121111 1)1( baba , 21121111 1)1( abab
21221121 )1( baba , )1( 22121211 abab
11212122)1( baba , )1( 11212122 abab
1)1( 22221221 baba , 12212222 1)1( abab
Therefore, 1
1121121
111
1111111
1111 )1()1()1](1)1([)1( aabaaabab (A2)
Given (A2), we have
111
112112111
111111 )1()1( yaabyayb (A3)
Derivation of equation (11)
Using the relationship between gross output x and final demand y specified in equation (5), we
have
12122222212 )1( xaxayyy (A4)
Also using )1( 22121211 abab ,
1211212112122121
22211211211211212121222121212111 )()()1(xabvybvybv
yybvxabvxaybvxabvxabv
(A5)
Derivation of equations (19) and (20)
Based on equation (6):
22121211211211111 ybybybybx (A6)
1221221
12222 )1()1( aabab
A2
From the gross exports identity, we have:
111
111121
1111121
111 )1()1(),()1( yaxeayeax (A7)
Combining (A6) and (A7), we can easily show that
])1([
])1([
])1([)1(
111
11211221122212121121121
111
11221212112112111121121
111
11121121121
1121121
yaabybybybabvyaybybybybabv
yaxabveaabv
(A8)
which is the first pure double counted term in Country 1's gross exports accounting equation
(13) that is expressed as function of both countries’ final demand.
Also based on equation (6):
22221221212211212 ybybybybx (A9)
Also from gross exports identity,
221
222211
2222211
222 )1()1(),()1( yaxeayeax (A10)
Combining (A9) and (A10), we can show that the second pure double counted term in equation
(13) can be expressed as:
])1([
])1([
])1([)1(
221
22122112212122112112212
221
22222212212122112112212
111
22212212211
2212212
yaabybybybabvyaybybybybabv
yaxabveaabv
(A11)
An alternative way to decompose the two pure double counted terms:
Derivation of
equation (21):
Based on (A1), (A7) and (A9),
])1([])1([]})1([{]})1([{
])1([])1([)1()1(
)1]()1([)1]()1([)1]([)1]([
)1]()1[()1]()1[(
)1()1()1()1()1()1(
111
2112211221221
221221122112
121
11121211221211
22212122112
121
1121211221211
2212122112
211
22122112211221121
11211221122112
211
22122112221221121
11211221112112
211
22122112121121121
11211221212212
211
22122112122112121
11211221211211
211
2212212212121
1121122111
211
2212212121
1121121
yaabybayaabybaeaxaybaeaxayba
eaaebaeaaebaeaabaebaeaabaeba
eaabaabaeaabaabaeaabaabaeaabaaba
eaabaabaeaabaabaeaabaaeaabaa
eaabveaabv
(A12)
A3
Derivation of equation (18)
221
22111
11211
2212212121
1121121
221
22122112212111
11211221121
222212212111121121211
2212212121
1121121
221
22122112212111
11211221121
2222122121221121211112112221212111
211
2212212121
1121121221
22122112212
212211212111
11211221121221212111
22112112212112
)1()1()1(2)1(2])1([])1([
)()()1(2)1(2])1([2])1([2
)()()1(2)1(2])1([2
][])1([2][
yayaeaabveaabvyaabybvyaabybv
ybybvybybveaabveaabvyaabybvyaabybv
ybybybybvybybybybveaabveaabvyaabybv
ybybvyaabybvybybvxvxveeGDPGDPee
(A13)
Appendix B
The derivation of gross exports accounting equation in G country N sector Model
B.1. The G-country, N-sector ICIO Model
Assume a world with G-countries, in which each country produces goods in N
differentiated tradable sectors. Goods in each sector can be consumed directly or used as
intermediate inputs, and each country exports both intermediate and final goods to all other
countries.
All gross output produced by country s must be used as an intermediate good or a final
good at home or abroad, or
G
rsrrsrs YXAX )( , r,s = 1,2…. G (B1)
Where Xs is the N×1 gross output vector of country s, Ysr is the N×1 final demand vector that
gives demand in country r for final goods produced in s, and Asr is the N×N IO coefficient matrix,
giving intermediate use in r of goods produced in s. The G-country, N-sector production and trade system can be written as an ICIO model in
block matrix notation
GGGG
G
G
GGGGG
G
G
G YYY
YYYYYY
X
XX
AAA
AAAAAA
X
XX
21
22221
11211
2
1
21
22221
11211
2
1
, (B2)
and rearranging,
A4
GGGGG
G
G
G
rGr
G
rr
G
rr
GGGG
G
G
G Y
YY
BBB
BBBBBB
Y
Y
Y
AIAA
AAIAAAAI
X
XX
2
1
21
22221
11211
2
11
21
22221
11211
2
1
(B3)
where Bsr denotes the N×N block Leontief inverse matrix, which is the total requirement matrix
that gives the amount of gross output in producing country s required for a one-unit increase in
final demand in destination country r. Ys is a N×1 vector that gives the global use of s’ final
goods.
B.2. Value-added share by source matrix
Let Vs be the 1×N direct value-added coefficient vector. Each element of Vs gives the ratio of
direct domestic value added in total output for country s. This is equal to one minus the
intermediate input share from all countries (including domestically produced intermediates):
)( G
rrss AIuV , (B4)
Define V, the G×GN matrix of direct domestic value added for all countries,
GV
VV
V
00
0000
2
1
. (B5)
Multiplying these direct value-added shares with the Leontief inverse matrices produces the
G×GN value-added share (VB) matrix as equation (27) in the main text, it has the property:
uBVG
ssrs . (B6)
B.3. Decomposition of gross exports
Let Esr be the N×1 vector of gross bilateral exports from s to r.
srrsrsr YXAE rsfor (B7)
A country’s gross exports to the world equal
A5
G
srsrrsr
G
srsrs YXAEE )(* (B8)
From equation (29) in the main text we know that
s
G
rsr
G
rgr
G
gsg XXYB
11 1 (B9)
Therefore, following identity holds
G
rgr
G
gsgsss YBVXV
1 1
(B10)
Multiplying both sides of (B8) by (B6), we have
G
srsrrsr
G
sttst
G
srsrrsrssss
G
sttstssss YXABVYXABVEBVBVuE )()()( **
(B11)
Now we add and subtract VTs*, defined by equation (32) in the main text, to the first term on
RHS of (B11). This gives
gr
G
sr
G
gsgs
G
srsrrsrssssssss YBVYXABVVTEBV
1
** )( (B12)
Recall that
G
rsrrsrs YXAX
1
)( as defined in (B1), inserting it together with equation (B9) into
(B12) gives
)()(1
** gs
G
gsgssssssssssssssss YBXVYXAXBVVTEBV
(B13)
Where ssssss YXAX equals the difference between country s' gross output and gross output
sold in domestic market, i.e. what country s' gross exports to the world market;
gs
G
gsgs YBX
1
equals the difference between country s' gross output and its gross output finally
consumed at domestic market . By rearranging terms,
][])([1
** ssssgs
G
gsgssssssssssss YBYBVXIAIBVVTEBV
(B14)
Substitute IAIB ssss )( in equation (B14) by rs
G
srsr AB
(the property of inverse matrix, see
equation (B19) bellow) we have
A6
G
sr
G
srsrssrsrssrs
G
sr
G
ggrsgsssss XABVYBVYBVEBV
1*
(B15)
Insert (B15) into (B11) and rearrange terms, we obtain equation (34) in the main text.
B.4. Further partition of equation (34)
The term that measures double counting by intermediate goods trade in equation (34)
(
G
srsrssrs XABV ) can be further split into two parts: one is part of the home country's domestic
value-added that is first exported but finally returns home in its intermediate imports to produce
final goods and consumed at home, the other is a pure double counting portion due to two way
intermediate trade.
Using the relation *sssssss EXAYX , it is easy to show that
*11 )()( ssssssss EAIYAIX . (B16)
ssss YAI 1)( is the gross output needed to sustain final goods that is both produced and
consumed in country s, using domestically produced intermediate goods; deduct it from country
s' total gross output, what left is the gross output needed to sustain country s' production of its
gross exports. Therefore, the left hand side of equation (B16) has straightforward economic
meanings. We can further show that
ssss
G
srrssrssssssss YAIABYBYAI 11 )()(
(B17)
the last term in RHS of (B17) is the final gross output needed to sustain final goods that is both
produced and consumed in country s, but using intermediate goods that was originated in
country s but shipped to other countries for processing before being re-imported by the source
country in its intermediate goods imports (gross output sold indirectly in domestic market).
Given (B17), it easy to see
*11 )()( sss
G
srrssrsssss
G
srrssrs
G
srsrssrs EAIABVYAIABVXABV
(B18)
Equation (B17) can be proven by using the property of inverse matrix:
A7
I
II
AIAA
AAIAAAAI
BBB
BBBBBB
GGGG
G
G
GGGG
G
G
...00
0...00...0
...
...
...
...
...
...
21
22221
11211
21
22221
11211
we therefore have
rs
G
srsrssss ABIAIB
)( (B19)
Using (B19), we have
ssssssssssssssss YBYAIIAIBYAI 11 )]()([)( (B20)
This is also the proof of equation (40) in the main text.
Appendix C Computation details for numerical examples 1 and 2
ICIO table underline numerical example 1
Output Input
Intermediate Use Final Use
USA CHN USA CHN
Intermediate Input
USA 100 50 30 20
CHN 0 50 70 80
Value Added 100 100
Total Input 200 200
Computation details:
The Gross exports decomposition matrix
7.1063.933.937.106
67.106033.9303.534069.4660
80702030
33.1067.02
2221
1211
xxxx
A8
The value-added production and trade matrix
Decomposition results based on equations (13) and (14)
Terms in equation
(13) &(14)
USA CHN
Value-added exports
v1 20 46.7 v2 26.7 0
Return home value
v3 23.3 0 v4 0 0 v5 0 0
Foreign Value v6 0 23.3 v7 0 0 v8 0 0
Gross Exports E 70 70
VAX ratio 0.67 0.67
Since there is no foreign value-added in USA's production, the 30 unit of domestic final
demand are 100% its own value-added, just as its exports, so its GDP is equal to 100. For CHN,
the value-added in its exports and domestic final consumption also sum to 100. Both countries
have identical VAX ratios, but the reasons why value added exports smaller than the gross
exports are different; For USA, due to some of its own value added that is initially exported
returns home after being used as an intermediate input in CHN to produce final goods exports
back to USA ; For CHN, due to its production for exports uses FV: intermediate goods from the
USA which embeds USA’s value added; The return home VA (23.3) is a true value added for
USA ’s national account, part of its GDP, but it is a double counting in official trade statistics
and from China’s point of view.
3.537.467.463.53
7.1063.933.937.106
5.0005.0
VBY
A9
ICIO table underline numerical example 2 and computation details
The Input-Output (ICIO) Table for Case 1
Note: The unit is $100K unless otherwise noted. Output
Input
Intermediate use Final use Total Output
C1 C2 C3 C4 C5 USA C1 C2 C3 C4 C5 USA
C1 0 1 0 0 0 0 0 0 0 0 0 0 1
C2 0 0 2 0 0 0 0 0 0 0 0 0 2
C3 0 0 0 3 0 0 0 0 0 0 0 0 3
C4 0 0 0 0 4 0 0 0 0 0 0 0 4
C5 0 0 0 0 0 5 0 0 0 0 0 0 5
USA 0 0 0 0 0 0 0 0 0 0 0 15 15
Value added 1 1 1 1 1 10
Total input 1 2 3 4 5 15
Computation details for case 1
Direct input coefficient matrix: A=
0000003/100000
05/40000004/30000003/20000002/10
Direct value-added share: Av= 3/25/14/13/12/11
Final demand matrix: Y=
1500000000000000000000000000000000000
A10
Leontief Inverse: B=
10000015/51000015/45/4100015/35/34/310015/25/24/23/21015/15/14/13/12/11
Gross exports:
054321
E
As an illustration, we list how our approach computes each of the terms (v1 through v9) for
Country 5 (the country that exports to USA, not USA itself):
Term 1 (v1 in Country 5's gross exports):
0)00000(*1*5/155
555
r
G
rYBV
Term 2:
1
150000
15/50000*5/15
55
rr
G
rrYBV
Term 3:
0
00000000000000000000
15/50000*5/15 ,5
555 ,5
55
G
r
G
rtrtr
G
r
G
rtrtr YBVYBV
Term 4:
0
00000
15/50000*5/155
55
r
G
rrYBV
Term 5:
A11
00*)01(*
05/4
000
15/50000*5/1)( 155
155
5555
YAIABVG
rrr
Term 6:
05*)01(*
05/4
000
15/50000*5/1)( 1*5
155
5555
EAIABVG
rrr
Term 7:
0)00000(*
05/45/35/25/1
15/14/13/12/115 5
555 5
55
G
t
G
rrtt
G
t
G
rrtt YBVYBV
Term 8:
45*5/4
)15*1*3/10*1*00*1*00*1*00*1*0(*
05/45/35/25/1
15/14/13/12/11
)()(5 5
155
5 5
155
G
t
G
rrrrrrtt
G
t
G
rrrrrrtt YAIABVYAIABV
Term 9:
00*5/4
)0*1*3/14*1*03*1*02*1*01*1*0(*
05/45/35/25/1
15/14/13/12/11
)()(5 5
*1
555 5
*1
55
G
t
G
rrrrrtt
G
t
G
rrrrrtt EAIABVEAIABV
Similarly, we can decompose other countries’ gross exports, and obtain the results reported in the upper panel of table 1.
A12
The ICIO Table for Case 2:
Computation details for case 2
Direct input coefficient matrix: A=
00000015/1400000
014/1300000013/1200000012/1100000011/100
Direct value-added share: Av= 15/114/113/112/111/11
Final demand matrix: Y=
0000015000000000000000000000000000000
Output Input
Intermediate use Final use Total Output
USA C1 C2 C3 C4 C5 USA C1 C2 C3 C4 C5
USA 0 10 0 0 0 0 0 0 0 0 0 0 10
C1 0 0 11 0 0 0 0 0 0 0 0 0 11
C2 0 0 0 12 0 0 0 0 0 0 0 0 12
C3 0 0 0 0 13 0 0 0 0 0 0 0 13
C4 0 0 0 0 0 14 0 0 0 0 0 0 14
C5 0 0 0 0 0 0 15 0 0 0 0 0 15
Value added 10 1 1 1 1 1
Total input 10 11 12 13 14 15
A13
Leontief Inverse: B=
10000015/141000015/1314/13100015/1214/1213/1210015/1114/1113/1112/111015/1014/1013/1012/1011/101
Gross exports:
151413121110
E
Again, we list how our approach computes each of the terms (v1 through v9) for Country 5 (the country that exports final goods to USA, the 6th in the trading sequence): Term 1 (i.e., v1 in Country 5's gross exports):
1)000015(*1*15/166
666
r
G
rYBV
Term 2:
0
00000
00000*15/16
66
rr
G
rrYBV
Term 3:
0
000150000000000000000
00000*15/16 ,6
666 ,6
66
G
r
G
rtrtr
G
r
G
rtrtr YBVYBV
Term 4:
0
00000
00000*15/166
66
r
G
rrYBV
A14
Term 5:
00*)01(*
015/14
000
00000*15/1)( 166
166
6666
YAIABVG
rrr
Term 6:
015*)01(*
015/14
000
00000*15/1)( 1*6
166
6666
EAIABVG
rrr
Term 7:
14)000015(*
15/1415/1315/1215/1115/10
14/113/112/111/116 6
666 6
66
G
t
G
rrtt
G
t
G
rrtt YBVYBV
Term 8:
0)0*1*00*1*00*1*00*1*00*1*0(*
15/1415/1315/1215/1115/10
14/113/112/111/11
)()(6 6
166
6 6
166
G
t
G
rrrrrrtt
G
t
G
rrrrrrtt YAIABVYAIABV
Term 9:
0)14*1*013*1*012*1*011*1*010*1*0(*
15/1415/1315/1215/1115/10
14/113/112/111/11
)()(6 6
*1
666 6
*1
66
G
t
G
rrrrrtt
G
t
G
rrrrrtt EAIABVEAIABV
Similarly, we can decompose other countries’ gross exports, and obtain the results reported at the lower panel of table 1
A15
Appendix D: Detailed numerical example of a two country supply chain1
We now consider an example in which both countries export (and import) intermediate
goods in an inter-country supply chain. This example will show our accounting equation can
decompose a country's gross exports into various value-added and double counted components in
a way that is consistent with one’s intuition. We will also illustrate why and how our estimate of
VS1* in such a case differs from Daudin et al, why and how our estimate of the share of
domestic value-added (GDP) in exports differs from Johnson and Noguera's value-added to gross
exports ratio, and why and how our estimate of foreign value-added (GDP) in exports differs
from HIY's VS measure but our foreign content in exports generalizes it.
Suppose the world production and trade take place in five stages (in a year) as
summarized by Table D1. In Stage 1, perhaps a design stage, Country 1 uses labor to produce a
unit of Stage-1 output. This is exported to Country 2 as an input to Stage-2 production. In Stage
2, Country 2 adds a unit of labor to produce 2 units of Stage-2 output which are shipped back to
country 1 as an input to Stage-3 production. Country 1 adds another unit of labor to produce 3
units of Stage-3 output which are then exported to country 2 as an input to Stage-4 production.
In Stage 4, country 2 adds a unit of labor to produce 4 units of Stage-4 output which are shipped
back to country 1 as an input to Stage-5 production. The Stage-5 output is the final good. 3
units of the final good are exported to country 2, and 2 units are absorbed domestically in
country 1.
Suppose each unit of intermediate and final goods is worth $1. The total output in country
1 is $9, in country 2 is $6, the total value added (labor inputs) in the two countries is $3 and $2
respectively. The total exports from 1 to 2 and from 2 to 1 are $7 and $6, respectively; and the
exports of final goods from 1 to 2 and 2 to 1 are $3 and $0 respectively.
For this simple example of an international supply chain, we can decompose both
countries’ gross exports into value-added and double counted components by intuition without
using any equations. The intuitive decomposition is summarized in Table D2. We will then
verify that our exports decomposition formula produces exactly the same results.
1 We are grateful to Peter Dixon and Maureen Rimmer for helping us to develop this instructive example.
A16
Table D1 A two country supply-chain
Country 1 Country 2 Final
Demand Labor input
Imported input
Output Imported input
Labor input
Output Final Demand
Stage 1 in $1 Stage 1 out $1 Stage 2 in $1 $1 Stage 2 out $2 Stage 3 in $1 $2 Stage 3 out $3 Stage 4 in $3 $1 Stage 4 out $4 Stage 5 in $1 $4 Stage 5 out $5 $2 $3 Total $2 $3 $6 $9 $4 $2 $6 $3
We proceed as follows: Starting from the last stage (Stage 5), each country contributes $2
of value-added with their (previously produced) intermediate inputs, and Country 1 contributes
an additional $1 of labor input to produce a total of 5 units of the final good. We assume labor is
homogenous across countries. Since 2 units of the final good stay in Country 1 and 3 units are
consumed in Country 2, all the value-added embodied in intermediate inputs that are eventually
absorbed by each country should be split as 40% for country 1 and 60% for country 2, in
proportion to the units of the final good consumed by the two countries. Therefore, the total
value added exports from Country 1 to 2 are 0.6*$3=$1.8 (which is recorded in the cell in row
“total” and column 2a of Table D2). Similarly, Country 2’s exports of value added to 1 are
0.4*$2=$0.8 (which is recorded in the cell in row “total” and column 2b). Out of Country 1’s $7
of gross exports, the total amount of double counting, or the difference between its gross exports
and its value-added exports is $5.2 (=$7-$1.8). This is recorded in the cell in row “total” and
column 7a. Similarly, out of Country 2’s $6 of gross exports, the total amount of double
counting is $6-$0.8=$5.2, which is recorded in the cell in row “total” and column (7b).
The beauty of this simple example is that we can work out the structure of the double
counted values by intuition. Given what happens in Stage 5, we can split a country’s value
added in production in each of the earlier stages into the sum of value-added exports in that stage
(that is ultimately absorbed abroad) and the value added that is exported in that stage but returns
A17
home next stage as part of its imports from the foreign country. Then the amount of exports in
each of the first 4 stages that are double counted can be computed as each stage's gross output
minus value added exports in that stage. In Stage 1, Country 1’s domestic value added is $1
(recorded in the cell (S1, 1a)). Since we know by Stage 5, 40% of the final good stays in Country
1, and 60% is exported to Country 2, we can split the $1 of domestic value added into $0.6 of
Country 1’s exports of value added (recorded in the cell (S1, 2a)) and $0.4 of the domestic value
added that returns home in the next stage and eventually consumed at home in Stage 5 (recorded
in (S1, 3a)). Out of Country 1’s gross exports of $1 in Stage 1, the total double counted amount
is the difference between its gross exports and value added exports, or $1-$0.6=$0.4, as recorded
in (S1, 7a). In Stage 2, Country 2 uses $1 of intermediate good from Country 1 as an input
together with its additional $1 of labor to produce $2 exports. Its domestic value added is $1
(recorded in (S2, 1b)). Again, since we know the split of the final good consumption in the two
countries in Stage 5, we can split Country 2’s domestic value added into $0.4 of its exports of
value added (recorded in (S2, 2b)) and $0.6 of domestic value added that will return home in
Stage 3 and eventually consumed at home in Stage 5(recorded in S2, 4b)). Recall that out of $1
of intermediate good that Country 2 imports from Country 1, $0.4 will go back to Country 1 and
be consumed there eventually. This is recorded in (S2, 5b), which is numerically identical to (S1,
3a). The remaining $0.6 is double counted intermediate goods, and is recorded in (S2, 6b). This
can also be verified in the following way. Since we know Country 2’s gross exports in Stage 2 is
$2 but its value added exports are only $0.4, the total amount of double counting in this stage’s
gross exports must be the difference between the two, or $1.6 as recorded in (S2, 7b).Therefore,
the “pure double counted” portion of foreign intermediate good has to equal $1.6 (S2, 7b) -$0.6
(S2, 3b) - $0.4 (S2, 5b), which equals to $0.6, as recorded in (S2, 6b). This amount represents the
part of Country 1’s Stage 1 intermediate good exports that cross borders more than twice before
it can be embed in the final goods for consumption.
In Stage 3, Country 1 uses $2 of imported intermediate goods from Country 2 as an input
with its additional $1 of labor to produce $3 exports. Country 1’s domestic value added is $1 (S3,
1a). Again, because 60% of the final good will be eventually absorbed in the foreign country, the
$1 of domestic value added can be split into $0.6 of Country 1’s exports of value added (S3, 2a)
and $0.4 of the domestic value added that is exported in Stage 3 but will return in Stage 4 and
eventually consumed there in Stage 5(S3, 3a). Furthermore, the Stage 3 production does use
A18
imported intermediate good from the previous stage. The amount of foreign value added
embedded in its intermediate good imported from Country 2 that is not pure double counting
should be the same as Country 2’s domestic value added that is sent to Country 1 in Stage 2 but
returns home and will be eventually absorbed there. We know that amount is $0.6 (S2, 3b).
Therefore, the amount of foreign value added that is used in Country 1’s Stage 3 production for
exports and that will be eventually absorbed in Country 2 should be the same as $0.6 in (S3, 5a).
Because the value of Country 1’s stage 1 exports ($1) is already counted three times by
the time Stage 3 exports take place, we record that amount as a pure double counting item in (S3,
4a). Since we know out of $3 of Country 1’s gross exports in Stage 3, only $0.6 is exports of
value added that will eventually be absorbed abroad, $3-$0.6=$2.4 represents the total amount of
double counting in this stage’s gross exports, and is recorded in (S3, 7a). Out of the $1 foreign
value added from Stage 2, since the amount that will go back to the foreign country and is
absorbed there is 0.6 (S3, 5a), the amount of pure double counting must be $1-$0.6=$0.4, as
recorded in (S3, 6a).
One way to check the sensibility of our reasoning is to compare the total amount of
double counting in Stage-3 gross exports with the sum of the double counted components. Out of
Country 1’s $3 of gross exports in Stage 3, we know the total amount of double counting is $2.4
(recorded in (S3, 7a)). We can check that the sum of the double counted components in Country
1’s exports in this stage (the sum of (S3, 3a), (S3, 4a), (S3, 5a), and (S3, 6a)) is also $2.4.
We now move to Stage 4, when Country 2 combines $1 of domestic value (recorded in
(S4, 1b)) with $3 of intermediate goods imported from Country 1 in the previous stage, and
exports $4 of intermediate goods in gross terms to Country 1. Given that 40% of the final good
will be absorbed in Country 1 by stage 5, we can split Country 2’s $1 domestic value added in
this stage into $0.4 which is Country 2’s value added exports (S4, 2b), and $0.6 which is the
amount of its domestic value added that will return home in Stage 5 and be absorbed at home (S4,
3b). Country 2’s gross exports in this stage also contain 40% of County 1’s value added from the
previous stage, recorded as $0.4 in (S4, 5b).
A19
Table D2 Intuitive accounting for the gross export flows in the two country supply chain
Note: a. In stage 5, because Country 1 exports 3 units of the final goods and keeps 2 units at home, 40% of Country 1’s domestic value added (or $0.4) in that stage stays home, and 60% of it (or $0.6) is its exports of value added to Country 2. The last row shows the concordance between the second to the last row of this table and the decomposition results reported in Table D4 that are derived from our gross exports accounting equations. The gross exports accounting equations (13) and (14) provide the final decomposition results as the total row in the table, not the intermediate iteration in each the stage.
From Country 1’s Viewpoint From Country 2’s Viewpoint
Domestic
Value-added
In exports
A Value-added
exports
Previous Intermediate
exports returning home
Foreign intermediate
imports
Total double counted
intermediate in exports
Domestic
Value-added in exports
Value-added
exports
Previous Intermediate
exports returning home
Foreign intermediate
imports
Total double counted interme-diate in exports DV
Pure Double
counting FV
Pure Double
counting DV
Pure Double
counting
FV
Pure Double
counting
(1a) (2a) (3a) (4a) (5a) (6a) (7a) (1b) (2b) (3b) (4b) (5b) (6b) (7b) Stage 1 (S1):
Country 1 exports and Country 2 imports
1 0.6 0.4 0 0 0 0.4
Stage 2 (S2): Country 2 exports and
Country 1 imports 1 0.4 0.6 0 0.4 0.6 1.6
Stage 3 (S3): Country 1 exports and
Country 2 imports 1 0.6 0.4 1 0.6 0.4 2.4
Stage 4 (S4): Country 2 exports and
Country 1 imports 1 0.4 0.6 1 0.4 1.6 3.6
Stage 5 (S5): Country 1 exports and
Country 2 imports 0.6 a 0.6 0 1.2 0.6 0.6 2.4
Total 2.6 1.8 0.8 2.2 1.2 1 5.2 2 0.8 1.2 1 0.8 2.2 5.2
Terms in Table D4 that correspond to the
previous row DV1 v1+v2 v3+v
4 v5 v6+v7 v8 Sum of v3 to
v8 DV2 v1+v2 v3+v4 v5 v6+
v7 v8 Sum of v3 to v8
A20
By symmetry, the pure double counting amount in (S4, 4b) must be the same as (S3, 4a),
which is $1. Let us next work out the pure double counting term in (S4, 6b). First, out of Country
2’s $4 gross exports in Stage 4, only $0.4 is value added exports, we know the total amount of
double counting must be $3.6, which is recorded in (S4, 7b). Second, we also know $3.6 of the
total amount of double counting must be equal to the sum of the double counted components, or
the sum of (S4, 3b), (S4, 4b), (S4, 5b) and (S4, 6b). This implies that (S4, 6b) should be $1.6.
The economic meaning of (S4, 6b) is repeated double counting of the intermediate goods that
have been double counted in previous rounds of trade.
We now go to Stage 5. Because this is the final stage in which the final good is produced
by Country 1 but distributed 40% and 60% in Countries 1 and 2, respectively, we record the
values somewhat differently from the earlier stages (when the entire production was exported).
While Country 1’s domestic value added in the production is $1 in this stage, only 60% of the
final good is exported. So we record the amount of domestic value-added in Country 1’s exports
as $0.6 (S5, 1a). The amount of Country 1’s value added exports (that is absorbed in Country 2)
is also $0.6, as recorded in (S5, 2a).
Since Stage 5 production uses imported intermediate good from the previous stage, it
embeds foreign value added from Stage 4. The amount of foreign value added from Stage 4 that
is used in Country 1’s Stage 5 production and eventually absorbed in the foreign country is
proportional to the amount of the final good that is exported from Country 1 to 2. This means (S5,
5a) is $0.6. This of course is the same value as in (S4, 3b).
To determine the value in (S5, 4a), we note that the total value added from Country 1 in
the first and the 3rd stages are $1. Both values are counted as part of Country 2’s intermediate
exports in Stage 4. Since only 60% of the final good are exported, the pure double counting
associated with the domestically produced intermediate goods in the previous stages is $2*0.6 =
$1.2.
To determine the value of (S5, 6a), we first note that the total amount of double counting
in Stage 5 exports is the difference between the value of gross exports in that stage ($3) and the
value added exports in that stage ($0.6), which is $2.4, as recorded in (S5, 7a). The value in (S5,
6a) would simply be the difference between $2.4 and the sum of the values in (S5, 2a), (S5, 4a),
and (S5, 5a), which yields $0.6. The amount in (S5, 6a) represents the value that is originally
A21
created in Country 2 but has been counted multiple times beyond the value added of Country 2
already assigned to Countries 1 and 2.
We can check the sensibility of the discussion by summing over the values across the five
stages. For example, when we sum up the values over all stages in Column (2a), we obtain 1.8,
which is exactly the amount of Country 1’s value added exports that we intuitively think should
be. Summing up the values in Column (7a) across the five stages yields $5.2, which is the same
as what we obtain intuitively earlier.
Separately, we can apply our decomposition formula and generate the measurements of
the same set of economic concepts. To do so, we note that the five stages in this example are best
represented by 5 sectors (e.g., car windows, paint on a car, rubber tires on a car and a whole car
are considered in separate sectors), because an input output table is built on the assumption that
all goods within a sector are homogenous, i.e the input-output and direct value-added
coefficients are the same for all products within a sector. In our example, because different
stages of the production have different direct value-added and IO coefficients, we have to treat
the five stages as five different sectors.
The inter-country supply chain data in table D1 can be summarized by the following
Input -output IO table:
Table D3 IO table constructed from two-country Supply Chain data
Output
Input
Intermediate use Final use Total output
Country 1 Country 2 Country 1 Country 2
Sector 1 Sector 2 Sector 3 Sector 1 Sector 2
Intermediate input Country 1 Sector 1 1 1
Sector 2 3 3
Sector 3 2 3 5
Country 2 Sector 1 2 2
Sector 2 4 4
Value-added 1 1 1 1 1
Total Input 1 3 5 2 4
Note: an input -output table is built on homogenous products assumption, i.e input-output and direct value-added coefficients are the same for each product/industry. In order to use an input-output model, each stage of production has to be treated as a distinct product/industry because different stages of the production has different direct value-added and IO coefficients. From table D3, we can obtain following matrixes:
A22
005/4000003/2000000
4/3000002/1000
A
In A,
000000000
11a ,
004/30
02/1
12a ,
5/40003/20
21a ,
0000
22a
Value-added coefficient:
5/13/111 v , 4/12/12 v
Final goods and exports
200
11y ,
300
12y ,
00
21y ,
00
22y ,
331
12e ,
42
21e
Leontief inverse B = ( I – A ) -1
105/4002/115/23/20
001004/305/3104/12/15/13/11
B
In B,
1005/3105/13/11
11b ,
004/304/12/1
12b ,
5/4005/23/20
21b ,
102/11
22b
And
100010001
)1( 111a ,
1001
)1( 122a
Equations (13) and (14) can be converted to a 5-sector version easily by defining each of their
terms in a matrix with proper dimensions. The formula in Equations (13) then allows us to
decompose Country 1’s gross exports as follows:
A23
v1= 8.1300
5/33/21300
1005/3105/13/11
5/13/1112111
ybv
v2= 000
004/304/12/1
5/13/1122121
ybv
v3= 000
004/304/12/1
5/13/1121121
ybv
8.0200
100010001
5/23/10
200
100010001
5/40003/20
004/304/12/1
5/13/11)1(4 111
1121121
yaabvv
2.2331
100010001
5/23/10
331
100010001
5/40003/20
004/304/12/1
5/13/11)1(5 121
1121121
eaabvv
v6= 2.1300
5/23/10300
5/4005/23/20
4/12/112212
ybv
v7= 000
1001
004/30
02/1
5/4005/23/20
4/12/1)1( 221
2212212
yaabv
A24
142
1001
004/30
02/15/23/10
42
1001
004/30
02/1
5/4005/23/20
4/12/1)1(8 211
2212212
eaabvv
Similarly, we can also decompose country 2's gross exports into the 8 terms specified in
equation (14). We summarize all the computation in table D4. It can be checked easily that the
numbers in Table D4 generated by our formula match exactly with the corresponding ones that
one can intuitively work out in Table D2. In particular, Country 1’s value added exports (that are
absorbed abroad) from our formula in Table D4 are $1.8, exactly as that in Table D2. In
comparison, the total domestic value added in Country 1’s exports (that does not exclude
exported value added that returns home but does exclude the pure double counted term) is $2.6.
This example confirms our theoretical discussion that value-added exports are generally smaller
than domestic value-added (GDP) in exports and domestic content in exports. If one is interested
in the share of domestic value added in a country’s exports, then the VAX ratio is not the right
metric.
From Table D4, the VS measure produced by our decomposition formula (13) is 2.2. The
intuitive discussion in connection with Table D2 illustrates why we argue that the VS measure is
not a 'net' concept and is not equal to foreign value added in a country’s gross exports. The
fundamental reason is that the VS measure has to include some pure double counted terms.
(Again, these pure double counting terms would disappear if we use the HIY assumption that at
least one of the countries does not export intermediate good.)
The more intermediate trade crosses border, the larger these double counted foreign
intermediates imports are. With two-way intermediate trade, the part of foreign GDP that is
embodied in the home country's gross exports will always be smaller than the VS measure.
Relative to the original VS measure, our generalized measure includes double counted
intermediate exports produced by the foreign country that may cross border several times (v8).
The numerical results also show HIY's convention that a country's gross exports is equal to
A25
domestic content plus vertical specialization is also maintained by our accounting equation (as
long as one defines domestic content and vertical specialization appropriately).
Finally, this example also shows that if one only considers returning domestic value-
added in final goods, while excluding domestic content returning home via intermediate goods
imports, such as Daudin et al (2011), then one would under-estimate VS1*. In this example, if
one applies Daudin et al’s narrow definition of VS1*, it would be zero as indicated by v3 in
Table D4. If one also includes returning domestic value added in intermediate good and a pure
double counting term, VS1* would become $3 instead. Our redefined measure of VS1* is more
complete.
Table D4 Gross exports decomposition based on our accounting equation
Terms in accounting equation E12 E21
v1= 12111 ybv 1.8 0
v2= 22121 ybv 0 0.8
v3= 21121 ybv 0 1.2
v4= 111
1121121 )1( yaabv 0.8 0
v5=12
11121121 )1( eaabv 2.2 1
v6= 12212 ybv 1.2 0
v7= 221
2212212 )1( yaabv 0 0.8
v8= 211
2212212 )1( eaabv 1 2.2
E=Gross exports (sum v1 to v8) 7 6 VT=Value-added exports (sum of v1 and v2) 1.8 0.8 DV=Domestic value-added in gross exports (sum of v1 to v4) 2.6 2 FV=Foreign value-added in gross exports (v6+v7) 1.2 0.8 DC=Domestic content in gross exports (sum of v1 to v5) 4.8 3.0 Double counted home country's intermediate exports 2.2 1 Double counted foreign country's intermediate exports 1 2.2 VS=Vertical specialization(sum v6 to v8) =v1b12 2.2 3
VS1* measure defined in this paper (sum v3 to v5) 3 2.2 VS1* measure defined in Daudin, et al. (v3 only) 0 1.2 Johnson & Noguera's VAX ratio 0.257 0.133 Share of domestic value-added in gross exports 0.371 0.333 Share of domestic content in gross exports =v1b11 0.686 0.5
Source: Authors’ estimates
A26
Appendix E Detailed results of magnification of trade costs by multi-stage production
As discussed in section 4.2 in the main text, our gross export accounting method provides
an ideal way to re-examine the magnification effect of trade cost by multi-stage production. In
Table E1, we first report standard tariffs (on a country’s exports) in columns (1a). These are
trade-weighted tariff rate applied by a country’s trading partners (in ad-valorem equivalent).
Column (2a) reports the share of imported content in final goods exports. These imported
intermediate inputs are used to produce final goods exports, and so incur multiple tariffs charges.
These tariff rates on the imported inputs (as a share of f.o.b. export value) are presented in
columns (3a); they are trade-weighted average tariffs for intermediate inputs from the other 25
countries/regions in our database that are used in the exporting country to produce final goods
exports. The sum of the two tariffs is reported in Column (4a).
Columns (5a) reports our illustrative calculation of the first order magnification effect of
using imported intermediate inputs to produce exports. It represents the magnification effect if
tariffs were the only factor that augments the trading costs. For instance, one additional stage of
production increases trade costs of Vietnam’s merchandise production by 80% of its standard
tariff.
Although the number is already quite high for a number of countries, these values still
represent only the lower bound of the true multi-stage tariff charge. First, in this illustration, we
only consider two stages of production, while in the real world, these inputs may have already
crossed multiple borders before reaching the final exporter. Second, we ignore transport costs in
this example, but transport costs are also magnified as intermediate goods cross multiple borders.
The second magnification force occurs because tariffs are applied to gross export values
instead of the value added in the direct exporting country. Table E1 also reports the
magnification ratio of the “effective” tariff rate to the standard tariff rate. Column (6a) reports
the effective tariff rate, which equals the standard tariff rate in column (2a) divided by the
domestic content share (which is 1 minus column (2a)) and weighted by trade. Column (7a)
reports the implied magnification ratio due to the presence of vertical specialization. These
effects are generally larger than the tariff magnification factor reported in column (5a).
A27
Generally speaking, tariffs play a large role in the magnification of trade costs in the
presence of GVCs for emerging market economies, while they play a smaller role for most
developed countries. The fact that the domestic value added share in emerging economies’
merchandise exports is usually lower than that in developed countries tends to amplify the
effective trade cost for developing countries. As an implication, reducing tariffs and nontariff
barriers in manufacturing sectors globally is fully consistent with the interest of emerging market
economies because it lowers the cost of GVC participation for developing countries. Lowering
“own” tariffs on intermediate inputs for domestic manufacturing production would significantly
reduce the magnification effects as demonstrated in column (5), while lowering such tariffs in
other countries would significantly reduce the effective rate of protection, as seen in columns (6)
and (7), due to the lower domestic value-added share in most developing countries’
manufacturing exports.
To see if the end-use classifications and the proportionality assumption produce different
results, we go through the same set of calculation but using the proportionality assumption to
construct our data set. All the estimates in Columns (1b), (2b), …,(7b) are the direct counterparts
to Columns (1a), (2a), …, (7a). In Column 8, we report the difference in terms of % of each
country's gross exports for the magnification factor computed using the two different databases.
For Indonesia, Malaysia, and China, the BEC method produces a larger magnification effect. In
comparison, for Canada, India, and Mexico, the BEC method produces a smaller magnification
effect. In general, which method we use makes a difference.
A28
Table E1 Magnification of trade costs on final goods exports from vertical specialization, 2004
Source: Authors’ estimates.
Database produced by BEC classification Database produced by proportion assumption 100* difference
Country or
region
Standard Tariff
Foreign content share (VS)
Tariff on imported
inputs
two stage tariffs 1a+3a
Magnifi-cation factor 4a/1a
Effective tariff rate
Magnifi-cation ratio 6a/1a
Standard Tariff
Foreign content share (VS)
Tariff on imported
inputs
two stage tariffs 1b+3b
Magnifi-cation factor 4b/1b
Effective tariff rate
Magnifi-cation ratio 6b/1b
Magnifi-cation factor 5a-5b
Magnifi-cation ratio 7a-7b
(1a) (2a) (3a) (4a) (5a) (6a) (7a) (1b) (2b) (3b) (4b) (5b) (6b) (7b) (8) (9) Advanced economies Aus-New Zealand 15.55 0.13 0.34 15.89 1.02 27.00 1.74 13.48 0.15 0.55 14.03 1.04 26.02 1.93 -1.9 -19.4
Canada 1.60 0.38 0.24 1.84 1.15 7.05 4.41 1.36 0.38 0.30 1.66 1.22 7.52 5.53 -7.1 -112.3
Western EU 6.16 0.12 0.24 6.40 1.04 12.09 1.96 6.06 0.13 0.24 6.30 1.04 12.22 2.02 -0.1 -5.4
Japan 6.22 0.12 0.05 6.27 1.01 11.19 1.80 6.36 0.12 0.06 6.42 1.01 11.42 1.80 -0.1 0.3
USA 4.38 0.13 0.17 4.55 1.04 9.19 2.10 4.05 0.15 0.21 4.26 1.05 9.26 2.29 -1.3 -18.8
Asian NICs
Hong Kong 10.16 0.42 0.00 10.16 1.00 27.91 2.75 10.02 0.40 0.00 10.02 1.00 26.09 2.60 0.0 14.3
Korea 6.05 0.32 1.46 7.51 1.24 17.32 2.86 6.34 0.35 1.74 8.08 1.27 19.62 3.09 -3.3 -23.2
Taiwan 4.76 0.42 1.40 6.16 1.29 20.08 4.22 4.45 0.43 1.40 5.85 1.31 19.56 4.40 -2.0 -17.7
Singapore 3.60 0.70 0.00 3.60 1.00 30.05 8.35 3.22 0.72 0.00 3.22 1.00 30.75 9.55 0.0 -120.2
Emerging Asia
China 6.17 0.29 1.91 8.08 1.31 21.42 3.47 6.44 0.29 1.97 8.41 1.31 21.86 3.39 0.4 7.7
Indonesia 7.53 0.30 1.34 8.87 1.18 24.39 3.24 9.44 0.27 1.28 10.72 1.14 26.65 2.82 4.2 41.6
Malaysia 3.55 0.46 2.11 5.66 1.59 20.93 5.90 4.38 0.45 2.50 6.88 1.57 23.04 5.26 2.4 63.6
Philippines 5.57 0.39 1.07 6.64 1.19 22.47 4.03 3.50 0.42 0.94 4.44 1.27 16.52 4.72 -7.6 -68.6
Thailand 8.16 0.40 4.23 12.39 1.52 36.54 4.48 7.67 0.41 4.36 12.03 1.57 35.05 4.57 -5.0 -9.2
Vietnam 10.71 0.43 8.62 19.33 1.80 55.10 5.14 10.29 0.45 9.17 19.46 1.89 54.52 5.30 -8.6 -15.4
India 7.82 0.18 2.98 10.80 1.38 22.08 2.82 6.93 0.19 3.10 10.03 1.45 19.82 2.86 -6.6 -3.6
Other emerging economies
Brazil 12.27 0.13 1.22 13.49 1.10 22.77 1.86 11.82 0.13 1.12 12.94 1.09 25.07 2.12 0.5 -26.5
EU accession 2.41 0.34 0.55 2.96 1.23 12.67 5.26 2.18 0.36 0.57 2.75 1.26 12.24 5.61 -3.3 -35.7
Mexico 0.88 0.31 1.00 1.88 2.14 6.36 7.23 0.67 0.30 1.02 1.69 2.52 5.73 8.55 -38.6 -132.5
Russian 5.36 0.18 1.61 6.97 1.30 17.23 3.21 3.64 0.16 1.34 4.98 1.37 14.86 4.08 -6.8 -86.8
South Africa 7.15 0.20 1.11 8.26 1.16 22.11 3.09 6.75 0.22 1.18 7.93 1.17 20.94 3.10 -2.0 -1.0
A29
Appendix F The difference between bilateral trade imbalance in gross and value-added
terms
Figure F1 provides a scatter plot of the trade balance in value added terms against the
trade balance in standard trade statistics for all bilateral country pairs in our ICIO database.
Without loss of generality, the two countries in any pair are always ordered in such a way that
the trade balance in gross terms is non-negative. A negative value-added to gross BOT ratio
indicates there is a sign change between BOT measured in gross and value-added terms. All
observations that lie below the 45 degree line have their bilateral trade imbalance smaller in
value-added terms than those in gross terms, and vice visa for observations that lie above the 45
degree line.
Zooming in near the origin shows that the trade balances of a number of country pairs
even have opposite signs measured in value-added and gross terms. For example, Japan’s trade
balance vis-à-vis China is switched from a surplus in gross trade terms to a deficit in value added
terms. This is consistent with the notion that a significant part of Japan’s exports to China are
components used by China-based firms for exports to the United States, the European Union and
other markets. This further illustrates potentially misleading nature of gross bilateral trade
imbalances.2
2Figure F1 also shows that the Korea-China-U.S. triple trade relationship is similar to the Japan-China-U.S. one.
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Figure F1: Gross and VA Balance of Trade, 2004
Note: The first country labeled in each pair is the surplus country while the second runs a deficit. Numbers in parentheses are the ratio of value-added to gross surplus.